Intermediate Mathematics

Finding the Part by Using Number Sentences

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Finding the Part by Using Number Sentences

The previous lessons showed how to solve percent problems using proportions. This lesson and the following two lessons give another method using number sentences.

This statement about percents:
n percent of the whole is equal to the part

can be written as the number sentence: n% × whole = part

Finding the Part by Using Number Sentences

Recall that all percent problems have three common elements:

the percent
the whole or total
the part

Using the standard number sentence for percent,

n% × whole = part,

the number sentence above translates to this multiplication sentence:

0.2 × 60 = 12

Finding the Part by Using Number Sentences

Here are four steps for using number sentences to solve percent problems:

1. Identify the three elements of the percent problem: percent, whole, and part.

2. Write a number sentence using the form
n% × whole = part.
If "n%" is known, write it in its decimal form.

3. Solve the number sentence.
If the "part" (the product of the multiplication sentence) is missing, multiply to find the product.
If "n%" or the "whole" (a factor of the multiplication sentence) is missing, divide to find the missing factor.

4. Answer the question in the problem.

Finding the Part by Using Number Sentences

Jesse gave away 25% of his models. If he had a total of 40 models to begin with, how many did he give away?

Identify the three elements of the percent problem: percent, whole, and part.

In this case, the percent is 25%; the whole follows the word "of" and is 40 models; and the part is unknown.

Write a number sentence using the form n% × whole = part.

Using the decimal form of the percent, the number sentence is 0.25 × 40 = part.

Finding the Part by Using Number Sentences

Jesse gave away 25% of his models. If he had a total of 40 models to begin with, how many did he give away?

Solve the number sentence.

To solve 0.25 × 40 = part, notice that the unknown quantity is the product of the multiplication sentence.
Therefore, multiply:

Answer the question in the problem.

Jesse gave away 10 of his models.

Finding the Part by Using Number Sentences

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Mary needs 50% of a dozen eggs for a recipe. How many eggs does Mary need?

Question 1 of 8

Change 50% to a decimal. Solve the number sentence 0.50 × 12 = part. Try again.

50% × 12 = part
0.50 × 12 = 6.00
Mary needs 6 eggs for the recipe.

Change 50% to a decimal. Solve the number sentence 0.50 × 12 = part. Try again.

One of these is the missing number in 0.50 × 12 = part. Try again.

Use "n% × whole = part" as the number sentence. Multiply to find the part.

Finding the Part by Using Number Sentences

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Joey had 250 baseball cards in his collection. He sold 20% of them. How many cards did he sell?

Question 2 of 8

Change 20% to a decimal. Solve the number sentence 0.20 × 250 = part. Try again.

20% × 250 = part
0.20 × 250 = 50.00
Joey sold 50 cards.

Change 20% to a decimal. Solve the number sentence 0.20 × 250 = part. Try again.

One of these is the missing number in 0.20 × 250 = part. Try again.

Use "n% × whole = part" as the number sentence. Multiply to find the part.

Finding the Part by Using Number Sentences

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Robin has a doll collection. If 30% of her 40 dolls are from foreign countries, how many of the dolls are from foreign countries?

Question 3 of 8

Change 30% to a decimal. Solve the number sentence 0.30 × 40 = part. Try again.

30% × 40 = part
0.30 × 40 = 12.00
Robin has 12 dolls from foreign countries.

One of these is the missing number in 0.30 × 40 = part. Try again.

Use "n% × whole = part" as the number sentence. Multiply to find the part.

Finding the Part by Using Number Sentences

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Mr.Davis gives 10% of his income to charity. He gets paid twice a month, and each paycheck is $1,000. How much money does he give to charity each month?

Question 4 of 8

Because he gets paid twice a month, he earns $2,000 per month. The "whole" is $2,000. Try again.

10% × (2 × $1000) = part
0.10 × $2000 = $200.00
He gives $200 to charity each month.

Change 10% to a decimal. Solve the number sentence 0.10 × $2000 = part. Try again.

One of these is the missing number in 0.10 × $2000 = part. Try again.

Use "n% × whole = part" as the number sentence. Multiply to find the part.

Finding the Part by Using Number Sentences

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A to Z Phone Answering Service answers about 3,000 calls each day. Of these calls, 0.5% are wrong numbers. About how many mistaken calls does the answering service receive each day?

Question 5 of 8

Change 0.5% to a decimal. Solve the number sentence 0.005 × 3000 = part. Try again.

0.5% × 3000 = part
0.005 × 3000 = 15.000
The answering service receives about 15 mistaken calls per day.

One of these is the missing number in 0.005 × 3000 = part. Try again.

Use "n% × whole = part" as the number sentence. Multiply to find the part.

Finding the Part by Using Number Sentences

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Steve's job is to drive people to medical appointments. Last year, he drove 460 people. This year, he drove 20% more people than he did last year. How many more people did he drive this year?

Question 6 of 8

Change 20% to a decimal. Solve the number sentence 0.20 × 460 = part. Try again.

20% × 460 = part
0.20 × 460 = 92.00
Steve drove 92 more people this year.

This is the total number of people Steve drove this year. Find just the number more than last year. Try again.

One of these is the missing number in 0.20 × 460 = part. Try again.

Use "n% × whole = part" as the number sentence. Multiply to find the part.

Finding the Part by Using Number Sentences

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Mia is a fashion photographer. Each workday she "shoots" 400 pictures. Only 9% of these will be used. How many of the photos that Mia takes each day are used?

Question 7 of 8

Change 9% to a decimal. Solve the number sentence 0.09 × 400 = part. Try again.

9% × 400 = part
0.09 × 400 = 36.00
Only 36 of Mia's photos will be used.

Use "n% × whole = part" as the number sentence. Multiply to find the part.

Finding the Part by Using Number Sentences

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Dennis reads meters for the gas company. He goes to 75 homes per day. Usually, only 60% of the people are home to let him in. How many indoor gas meters is he able to read each day?

Question 8 of 8

Change 60% to a decimal. Solve the number sentence 0.60 × 75 = part. Try again.

60% × 75 = part
0.60 × 75 = 45.00
Dennis reads about 45 meters per day.

Use "n% × whole = part" as the number sentence. Multiply to find the part.

Finding the Part by Using Number Sentences