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Shortcuts with Percents and Fractions
Some problems can be solved more than one way. Thinking about the problem for a minute might allow you to find a shortcut for solving the problem. Sometimes it may help to think of a fraction instead of a percent, or vice versa. Sometimes a quick mental step will eliminate one of the math steps needed to be done on paper. Try some of these:

By taking a few seconds to think about the problem you may save yourself some time and effort!

Shopping in the Housewares Department
Small group work:
Divide class into 2 or 3 small groups.

1 copy of the bottom half of this page for each group.

weekly flyers or newspaper advertisements from area merchants that feature general household merchandise.

Have the students work in groups to make a list. After 15 minutes, compare lists.

You are moving into your first apartment, and you need to do some shopping. Your apartment has all of the necessary appliances, and your food will be purchased at a later date. You have brought some used furniture, a vacuum cleaner, dishes and towels.

What you need to do now is to purchase all the miscellaneous household items that you will need. You have budgeted $100 for these items.

With your group, make a list of items and estimated costs that you should plan to buy to keep your apartment clean and orderly.

Small Group Cooperative Problem Solving

Andrea, Bill, Carlos, and Donna go to the mall. Each has things in mind to purchase. They plan to meet at the food court at 3:30 to have a soft drink. Who has enough money left to treat for the soft drinks?
    Clue 1: At the start, Andrea has $50, Bill has $35, Carlos has $35, and Donna has $15.
Andrea, Bill, Carlos, and Donna go to the mall. Each has things in mind to purchase. They plan to meet at the food court at 3:30 to have a soft drink. Who has enough money left to treat for the soft drinks?
    Clue 2: Andrea finds the shoes she needs at Sports, Inc. for 30% off the regular price of $65.99. Tax is 5.5%.
Andrea, Bill, Carlos, and Donna go to the mall. Each has things in mind to purchase. They plan to meet at the food court at 3:30 to have a soft drink. Who has enough money left to treat for the soft drinks?
    Clue 3: Bill needs a gift for his mother's birthday, He decides to purchase a sweater at King's that is 1/4 off the regular price of $39.99, Tax is 5.5%. Gift wrapping is free, but he needs to use $2 for a card.
Andrea, Bill, Carlos, and Donna go to the mall. Each has things in mind to purchase. They plan to meet at the food court at 3:30 to have a soft drink. Who has enough money left to treat for the soft drinks?
    Clue 4: Carlos buys both of his 2 sons T-shirts that are $9.99 each, and a book for himself that is $4.99. Tax is 5.5%.
Andrea, Bill, Carlos, and Donna go to the mall. Each has things in mind to purchase. They plan to meet at the food court at 3:30 to have a soft drink. Who has enough money left to treat for the soft drinks?
    Clue 5: Donna finds a great bargain: Bed pillows at 2 for $26.99. However, she only needs 1 pillow. Tax is 5.5%.

Directions: Separate class into groups. Give paragraph and the clues to each group. Have group members do math computations to find group answer.

Andrea spends $48.73, Bill spends $33.64, Carlos spends $26.35, and Donna spends $14.25. Carlos has money left to treat for soft drinks.

Major Purchase and Shopping by Mail

Multiplying percents; using proportions; changing fractions to percents and percents to fractions; computing installment plan buying; learn to fill out catalog order forms; computing percents saved on sale items and comparing sales at various stores; and learning additional ways to save money.

Handouts, catalogs, sales, receipts, and newspaper advertisements.

Multilevel ABE and GED

Large, Small, Individual

1 hour for each handout.

Some introduction and prior knowledge of percents, fractions, and decimals needed. Explain installment plans. Use handout "Installment Plan Buying" for practice and additional discussion. Use catalogs and copies of "Mail Order Shopping." Discuss benefits and time saving features of mail order and disadvantages of shipping costs and not liking merchandise when it arrives! Teach proportions with handouts and additional example from newspapers. As a wrap-up to unit on shopping, discuss any other aspects not already covered, Use handout "Other Shopping Ideas."

Life Skills Mathematics, AGS, Ch. 13; Lifeskills: Developing Consumer Competence, Contemporary Ch. 3; Essential Mathematics for Life, Books 3,7,8, Glencoe.

*Installment Plan Buying*
Some stores will offer you the choice of buying large items on the installment Plan. This means they will ask for a down payment, and then a scheduled number of payments. The plan might read like this:

As a consumer, it is helpful to figure out how much you are paying in total. The store will usually be charging you an additional amount, called a finance charge. The store owner would like to make an additional profit since he will be giving you the product long before it is paid for. In the example above, your total cost for the mattress and box springs will be $550.00: $50.00 + (10 x $50.00 or $500.00) = $550.00.

Solve the following problems.

There definitely are some times when using the installment plan is necessary or the only way to make a purchase. However, there are some times when it should not be used.

*Mail Order Shopping*
When ordering by mail, it is important to be as neat and accurate as possible on the order form. The price column must be totaled, tax added when required, delivery costs added, and a grand total computed.

Use a catalog and pick out several items you would like to order. Enter all the required information on the form below. Finish all steps of the order.

City, State

Page No. Name of
Size Color How Many Price
for One
Total Price
for this Item
Amount for Delivery
Merchandise Total Delivery Charge
$.01 to $9.99$1.50
$10.00 to $19.99$2.50
$20.00 to $29.99$3.50
$30.00 to $39.99$4.50
$40.00 to $49.99$5.50
$50.00 and over$6.00
Merchandise Total
Amount for Delivery
(see chart)
Sales Tax @ 6.5%

*Using Proportions to Find Prices*
You may wish to find the price of a smaller or larger number of items than the advertised price reflects. You can do this with a proportion.

Example: The cost of green peppers is 2 for $.85. How much does 1 cost?

Step 1: Write a proportion.
2 = 1
$.85 n

Step 2: Solve for n. Multiply the 2 numbers that are opposite each other, and divide by the third number.
2 = 1 $.85 x 1 = $.85 n 2 $.425

Step 3: Round up to the next penny if there is a remainder:
$.425 = $.43

One green pepper costs $.43 cents.

Find the cost of the following items using proportion.

*More Uses of proportion and Percent*
There are many ways to use proportions and percents to solve problems. By filling in a formula with the 3 known figures, the fourth can be found.

Example: A CD player is marked down from $300.00 to $240.00, What is the percent of the discount?

Step I --Think: if the new price is $240.00, the discount = $60.00 (300 - 240 = 60)

Step 2 part = % $60.00 = % 60 x 100 = 20 whole 100 $300.00 100 300 The discount amount is 20%

Example: Tomas has returned home to live with his mother for a while. She asks him to give her 75% of his weekly earnings for room and board. If Tomas earns $122.50 per week, how much will he owe to his mother? part = % ? = 75% $122.50 x 75 = $91.8750 or $91.88 whole 100 122.50 100 100

Try some yourself! Use the formula above. Use your calculator!

*On Sale!*

A. Electric dryer $177 B. Gas range $197 C. Refrigerator $377
D. Microwave oven $89.86 E. 13" television $129

Sometimes stores will be having a sale and will advertise that some items or all items are discounted. However, they may not change the price tags on the items; instead, the sign might tell you that "the register will scan the correct price."

For items A-E above, compute the amount of money to be taken off the original price if the sign says:

*Buying With A Discount*
Store discounts can be expressed in percents or fractions. When comparing discount prices, it is important to be able to find out which discount will save you the most money. Sherman's and Major's are two appliance stores in the local area. Both sell the same brands of appliances. Circle the store offering the better discount:

1. Refrigerators 35% off at Sherman's 1/2 off at Major's
2. Washing machines 331/3% off at Sherman's 1/4 off at Major's
3. TVs 10% off at Sherman's 1/5 off at Major's
4. Cd players 60% off at Sherman's 2/3 off at Major's

To change from a percent to a fraction, drop the decimal point and put the number over 100. Reduce if possible. over 2 spaces to the right. 35% = 35 = 7 100 20 To change from a fraction to a percent, divide the denominator into the numerator. Move the decimal point 1 = 16 4/6 = 16 2/3 = 16 2/3% 6 6 1.00

Do the following conversions. Then use the fraction or the percent to find the sale price.

Appliance Fraction
Sale Price
Camera 1/3 $50.00 $
Toaster 25% $29.00 $
Oven 1/8 $499.00 $
VCR 2/3 $200.00 $
Headphones 15% $35.00 $
Video Game 2/5 $109.00 $

*Other Shopping Ideas*
1. Make time to do comparison shopping whenever possible. If only one store advertises the item you want, call other stores and ask over the telephone if the item is available and what the price will be. Sometimes a store will match a competitor's price.

2. Do comparison shopping frequently when you buy groceries. Find out which store has the better prices on items you use weekly. Buy on sale whenever you can and stock up on extra items while they are on sale.

3. Take a small calculator with you when you shop.

4. If you have to buy items on the installment plan, figure out how much additional money you will be spending. Think about delaying the purchase until you have the cash whenever possible.

5. Practice rounding and estimating when you are buying a small number of items. See how close you can come to the actual price rung up on the cash register.

6. Check your sales receipts often. Always check on larger items. Stores do occasionally make mistakes. Sometimes they forget to enter a sale price into the computer, and the register rings up the full price. If they make a mistake, call it to their attention, You will save money, and so will the customers after you!

7. Try some generic brands. You may find they are completely acceptable on most items.

8. Plan ahead for major purchases, birthday and holiday shopping. Try to buy some items in advance on sale. Or make purchases during clearance sales and save them for the next occasion.

9. If you must buy a larger quantity than you need of an item, think of ways to use the extra. Double the recipe and freeze some. Give the extra amount to your neighbor. Look for another recipe that also uses that item.

10. Using MATH can save you money!

Grocery Shopping

Practice adding, subtracting, multiplying, and dividing decimals; reducing and multiplying fractions; comparing fractions and decimals; computing total cost of food items; computing change; computing unit costs; computing costs with coupons and sales; comparing costs at different stores; changing fractions to percents, and cooperative learning.

Handouts and local grocery flyers, food products that come in various sizes.

ABE and GED-Multilevel

Large, Small, Individual

1/2 to 1 hour per handout.

Some instruction or prior knowledge of decimals and fractions needed. Distribute grocery store flyers to begin first day of discussion of grocery store shopping. Discuss bar codes on products and price locations, such as shelf edges, stamped price tags, and signs. Discuss general public's confusion on comparison shopping. Discuss coupons and rebates. Easiest hand- out should be "Shopping at Different Stores." Work in groups or individually. Use other handouts at following sessions as desired.

Life Skills Mathematics, A.G.S. Inc. Ch.8; Essential Math for Life, Glencoe, books 2,7,8; Math Matters for Adults, Steck-Vaugh, Fractions and Decimals, Math in the Supermarket, Educational Design Inc.

Shopping at Different Stores

Cranberry Drink, 64oz. $2.99 Happy Valley Salad Dressings $.99
Broccoli, per bunch $.79 Flora's Frozen Vegetables $.88
Macaroni & Cheese $.39 Raz Pineapple Chunks 20 oz $.79
All-Purpose Flour $.69
Macaroni & Cheese $ .44 Florals Frozen Vegetables $.99
Cranberry Drink,64oz.$2.99 Broccoli, per bunch $.88
Raz Pineapple Chunks $ .69 All-Purpose Flour $.99
Happy Valley Salad Dressings $1.99
A-U-Purpose Flour $.88 Cranberry Drink, 64 oz. 2/$5.00
Happy Valley Dressings $1.69 Broccoli, per bunch $.68
Flora's Frozen Vegetables$.79 Raz Pineapple Chunks, 20 oz $.79
Macaroni & Cheese $.69

1. Which of the three stores has the best total price for these 7 items?
What would be the change received from $20.00?

2. Sharon needs to buy 2 boxes of macaroni & cheese 1 bottle of cranberry drink, and 1 bunch of broccoli. What would be the best total price for these 3 items? store.
What would be the change received from $10,00?

3. Sam would like 3 bags of frozen vegetables for his homemade soup. He also needs a bag of flour, Which store would have the best total price? price.
What would be the chary received from $5.00?

4. You wish to purchase 2 bottles of salad dressing and 3 cans of pineapple chunks. Where should you shop for the best total price? price.
What would be the change from $20.00?

5. What other factors are important to consider besides price when deciding which store to do your grocery shopping?

*Comparing Prices*

1. What is the price of 24 cans of each of these special offers?
1. 2. 3. 4. 5.

2. Which offer is the least expensive? the most expensive?

3. If a $.50 coupon is used, which is the least expensive?
. If the coupon is doubled, which is the least expensive? .

4. If 2 $.50 coupons can be used, one for each 12 pack, which would be the best offer?

5. If only 12 cans are needed, which is the best offer?

6. If many 12 packs are needed, such as for a party, what would be some ways to save the most money?

Fruit Salad
The produce department of grocery stores contains fresh fruits and vegetables. Items can be sold by the pound, by the bunch, or by the piece.
Which fruits and vegetables have you seen sold by the pound?
Which are sold by the bunch?
Which are sold by the piece?

Many items may be prepackaged by the wholesaler before they.come to your store, such as radishes, carrots, or apples. What are some fruits or vegetables that are packaged by the produce department employees?

Most items can be bought in very small quantities. If you don't need or won't use 6 tomatoes wrapped in cellophane, ask the produce department worker to open the package for you. Buy the amount you will use during the next few days.

If grapefruit are priced at 4/$1.00, and you wish to purchase 1 grapefruit, how much will you pay?

Pick 4 fruits from those shown to make a fruit salad. Try to balance your salad with fruit of different colors and tastes. Try to have about the same amount of each fruit What will your total cost be?

Grapes $1.39 lb. Strawberries $.99 pt. Oranges 6/$.99
Grapefruit 4/$1.00 Cantaloupe $1.19 ea.
Pineapple $1.99 ea. Kiwi 3/$.99 Apples $89 lb.

*Price Per Ounce/Unit Price*
Sometimes stores will have the "price per ounce" listed on the tag on the edge of the shelf so that it is easy for you to see which size of a product is a better value, If it is not listed, you might want to figure it out for yourself.

Example: Rice cereal 14 oz. is $2.29 20 oz. is $2.99 2.290 = .163 2.990 = .149 14 or 16 per oz. 20 or l5 per oz. Therefore the 20 oz. size is a better deal.

Figure out some prices per ounce for yourself.

Small Size Large Size Better Deal
Apple Juice 32 oz./$.79 64 oz/$1.49
Pork Chops 1.5 lb./$2.79 2.5 lb./$4.99
Carrots 1 lb./$ .69 2 lb./$1.35
Potatoes 5 lbs./$1.89 10 lbs./$3.89
Ice Cream1 qt. (32 oz.)/$1.791/2 gal. (64 oz.)/$3.49
Ravioli (canned) 15 oz./$.89 23 oz./$1.29
Chicken Noodle Soup 10.5 oz./$.63 26 oz./$1.49
Cocoa Mix 12 oz./$.99 20 oz./$1.39
Milk 1/2 gal./$.95 1 gal./$1.89
Bagels 1/$.35 6/$1.99
Soda Pop6 12 oz. cans/$1.992 liter bottle/$1.29 (67.6 oz.)

Does your grocery store have unit prices listed by each item? Write a paragraph expressing your appreciation to the manager of the store. Be sure to include specific details about the way the unit prices help you as a consumer.

If your grocery store does not have unit prices listed, write a paragraph to the store manager. Explain how the unit prices would help you shop for the best value, Include specific examples.

*Staying Within A Budget*
Donna is going to have a small party Saturday night with a few friends. Because of her limited budget, she has made a list of food items she would like to be sure to purchase only what is needed at the grocery store. She is looking at the weekly flyer for Jones' Grocery Store to see how much her items will cost.

Donna's list Jones' weekly flyer Donna's cost
1/2 lb. sliced turkey turkey $4.99 lb
3/4 lb. sliced ham ham $3.99 lb.
1 1/2 lbs. muenster cheese muenster cheese $4.39 lb.
2 lbs. potato salad potato salad $1.59 lb.
8 sub buns
(hint: 8 is what part of a dozen?)
sub buns $2.29 doz.
1 bag chips chips 2/$4.99
2 bags pretzels pretzels $ .99
12 cans of pop pop 6/$1.99

Figure out the cost of the items on Donna's grocery list.
total cost.

Donna would also like to buy a small cake to celebrate one guest's birthday. Small cakes are $4.00. Donna has $30.00. Will she have enough money for the cake?

Comparing Unit Costs
Be a careful shopper Advertisements can fool you! The only way to find out which of brands is the least expensive is to use MATH. There are 2 ways to find the answer.

Smart Value pears are 2 cans for $.69.
Delicious pears are 3 cans for $ .99.
Which is the better value? Solution #1 Reduce the Fraction Solution #2 Division Problem Smart Value 69 cost - $.34 1/2 each Smart Value Divide 2 into .69 2 cans the answer is .34 1/2 each Delicious 99 cost - $.33 each 3 cans Delicious 33 each The same 2 ways can be used to figure out which size of a product is a better value: Your favorite cereal comes in 14 or 26 ounce package. Make a fraction with each size under the cost: cost cost Reduce the fraction to compare cost. 14 26 Or make a division problem.. Divide the cost by the number of ounces. cost cost 14 26 Either method will give you the price per ounce.

Smart Value Delicious Which is the better value?
Tissues 3/$2.00 8/$6.00
Bananas 4 lbs./$.99 3 lbs./$. 68
Yogurt 2/ .89 $.42 each
1 loaf bread $.65 each 2/$1429
Cupcakes 6/$1.49 $.25 each
Cereal 13 oz./$2.29 19 oz./$3.09
Pickles 8 oz./ $1.09 12 oz./$1.49
Milk 1/2 gal./$.97 1 gal./$1.89

*Tossed Salad*

Ellen wants to make 3 pounds of her favorite salad, How many ounces of each vegetable will be on her shopping list?
    Clue 1: Lettuce is 2 times the amount of any other vegetable.
Ellen wants to make 3 pounds of her favorite salad, How many ounces of each vegetable will be on her shopping list?
    Clue 2: 2/3 of the salad is green.
Ellen wants to make 3 pounds of her favorite salad, How many ounces of each vegetable will be on her shopping list?
    Clue 3: 1/6 of the salad is cucumbers. (Think of cucumbers as "green").
Ellen wants to make 3 pounds of her favorite salad, How many ounces of each vegetable will be on her shopping list?
    Clue 4: 1/6 of the salad is orange.
Ellen wants to make 3 pounds of her favorite salad, How many ounces of each vegetable will be on her shopping list?
    Clue 5: 1/12 of the salad is red.
Ellen wants to make 3 pounds of her favorite salad, How many ounces of each vegetable will be on her shopping list?
    Clue 6: Cauliflower will be the same amount as tomatoes.
Ellen wants to make 3 pounds of her favorite salad, How many ounces of each vegetable will be on her shopping list?
    Clue 7: Celery will be the same amount as carrots.

Directions: Separate class into groups. Distribute paragraph and clues to each group. Have group members do math computations to find group answer.


Lettuce = 16 oz. Cucumbers = 8 oz. Celery = 8 oz.
Carrots = 8 oz. Tomatoes = 4 oz. Cauliflower = 4 oz.

Taking The Stress Out Of The Holiday Budget

Allowing students to interact and learn to make good economical as well as nutritional choices when buying groceries for everyday or a holiday meal.

Food Pyramid; grocery ads; grocery tally
Advanced: grocery coupons

All Levels


Can be done in one class period or extended over two.

Students are given a copy of the food pyramid and the nutritional value of each section is explained. After dividing into small groups of 2-4, they are presented with several grocery ads. A budget is determined and a holiday is appointed to each group. Students must then decide what they are going to feed the family buying wisely from the grocery ads. They must have foods from each pyramid category without going over their grocery allowance, and they must buy enough to feed all 8 people. Students then write their menus on the board and need to show what they've bought and how much each item costs. The team coming the closest to serving a nutritional meal without going over their budget is the winner. Advanced: Follow the same procedure but add coupons (either ones you've saved or homemade) that co-ordinate with your ads. Then tell students that they may deduct the coupon from the item they're buying. To make it more difficult, double coupons up to $ 1.00. They must be able to show the deductions on the board when they write out their menu,

Grocery ads and manufacturers coupons. "Food pyramid" from ext. April 93 issue.

Holy COW! Look What We're Eating!

Make students aware of how much our society is eating as well as The nutritional values that could improve their own diet, Also teaching math skills from simple addition through fractions.

Food Pyramid; What Counts as a Serving? Rate Your Diet; Fast Food menus; Fast Food poster; general info concerning calories.

Information is valuable to all levels. Math is geared to ABLE Students.


Over a 20 hr. Week.

I. Students are given a copy of the food pyramid and the nutritional value of each section is explained. The hand-out, "What Counts As A Serving" is discussed and the instructor can show samples of a medium apple; 1/2 cup of rice; 2 oz. Of cheese, etc. Ask students to "Rate Their DieT" on the next handout and then by following the pyramid, list all the foods they've eaten on the previous day on the food pyramid.

II. Explain calories and why people gain weight. Show a sample fast food menu for a day. Make up questions for addition; subtraction; multiplication; fractions; etc.

III. Give students the correct amount of calories for a day for a woman or man and allow them to produce their own fast food menu. Advanced: Write your fast food menu for a day within the correct servings of the food pyramid.

Restaurant Menus/Hand-outs- "Harvest Health at Home" Ext. April, 1993, "Calories In Fast Food" Ohio Dept. of Health.

A look at the Food Pyramid
A guide to daily food choices.

Fats, Oils
and Sweets
use sparingly
Milk, Yogurt
and Cheese Group
2-3 servings
Meat, Poultry,
Fish, Dry Beans,
Eggs & Nuts Group
2-3 servings
Vegetable Group
3-5 servings
Bread, Cereal, Rice & Pasta Group
6-11 servings


The body uses energy all the time. You use up that energy when you do anything from sleeping to running. Different foods contain different amounts of calories. When a person is idle, they need less calories than one who is very active. You need more calories when you're sick than when you're ill. People gain weight when they eat more calories than their bodies use for energy. Calories - The energy in food is measured in calories. 3,500 calories per pound.

Nutrition - The foods needed by the body for growth.

In order to lose a pound, one must consume 3,500 less calories. This can be done by cutting back or by burning the calories off through exercise.

What Counts as 1 Serving?
The amount of food that counts as 1 serving is listed below. If you eat a larger portion, count it as more than 1 serving. For example a dinner portion (1 to 1-1/2 cups) of spaghetti would count as 2 or 3 -servings of pasta.

Try to pick the lowest fat choices from the food groups. No specific serving size is given for the fats, oils and sweets group because because the message is USE SPARINGLY.

Bread, Cereal,Rice and Pasta



Milk, yogurt, and Cheese

Meat, Poultry, Fish, Dry Beans, Eggs and Nuts

Rate Your Diet
Mark the box which best describes what you eat. (See above for serving sizes.)

Always Sometimes Never
I eat at least 6 servings
of bread, cereal, rice, pasta or
other foods made from
grains every day.
I eat at least 2 servings
of whole grain foods every day.
I eat at least 3 servings
of vegetables every day.
I eat cooked legumes,
like navy and kidney beans,
2 to 3 times a week.
I eat a dark green leafy
vegetable, like spinach or broccoli,
2 to 3 times a week.
I eat at least 2 servings
of fruit every day.
I eat at least 2 servings
of milk, yogurt or cheese every day.
I eat at least 2 servings
of meat, poultry, fish, dry beans,
eggs or nuts every day.

How Did You Do?
Add the number of boxes you checked in each column to rate your diet.

You have a bumper crop!
If you checked 8 answers in the first column, you are probably getting the nutrients you need. Keep up the good work!
Your harvest is near!
If you checked the most in the second column, you are on your way to choosing a healthy diet. READ ON TO LEARN MORE WAYS TO MAKE HEALTHY CHOICES.
Sorry, crop hailed out.
If you checked most answers in the third column, you need at least the minimum number of servings from all the food groups.


Breakfast McDonalds 3 Hotcakes w/butter, syrup
Coffee (2 cups)
Milk (1 cup)
Lunch Burger King Whopper
Fries, Regular
Side salad w/ranch dressing
Milkshake, vanilla
143 (60 + 83)
Dinner Ponderosa N.Y. Strip Steak
baked potato
stuffing (4 oz)
bread (I slice)
macaroni salad (3.5 oz)
fruit yogurt (4 oz)
iced tea
Snack Dairy Queen banana split (1/3) 180
Pizza Hut Personal Pan Pepperoni (1/2 pie)
cola (12 oz.)



Find the number of calories consumed if Proportions you drank 8 oz of cola (12oz =8 96 c 145 cal = ? cal) 145 x 8 = 1160 12/ 1160 you ate 6 oz of stuffing (1/2 3/4 675 9 cal) 675 x 3/4 = 5 10 510 1 510 2 1 2= 1 x 1=1020

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