Percent of a number

Here is everything you need to know about finding the percent of a number, including how to solve with or without a calculator.

Students will first learn about finding the percent of a number as part of ratios and proportions in 6th grade.

What is a percent of a number?

The percent of a number can be calculated using a variety of different methods.

For example, what is 35\% of 60?

Method 1: Using ratios

Start with 60, which is the whole, or 100\%, and work down the table using ratios.

Percent of a Number image 1

Now use the ratios in the table to find 35\%.

10 \% \times 3=30\% and 6 \times 3=18, so 30\% is 18 and the table shows that 5\% is 3.

\begin{aligned} 35\% \text{ of } 60 &= 18 \, + \, 3=21 \\ & \quad \; ↑ \quad \;\; ↑ \\ & \;\; 30\% \, + \, 5\% \end{aligned}

Method 2: Using equivalent fractions

Write the percent as a fraction in its lowest terms and then multiply the number by this fraction.

35\% = \cfrac{35}{100} =\cfrac{7}{20}

60 \times \cfrac{7}{20} = \cfrac{60\times 7}{20} = \cfrac{420}{20} =\cfrac{42}{2}= 21

Method 3: The one percent method

Find 1\% first by dividing the amount by 100 and then multiply the percent (as a whole number).

60 \div 100 \times 35=21

Note, this works because 60 \div 100 \times 35=60 \times \cfrac{35}{100}.

Method 4: The decimal multiplier method

First, convert the percent into a decimal, and then multiply the amount by this decimal.

35\%=0.35

60 \times 0.35=21

Methods 1 and 2 lend themselves to questions where a calculator is not allowed.

Methods 3 and 4 lend themselves to questions where calculators are allowed.

What is a percent of a number?

What is a percent of a number?

Common Core State Standards

How does this relate to 6th grade math?

  • Grade 6 – Ratios and Proportional Relationships (6.RP.A.3c)
    Find a percent of a quantity as a rate per 100 (for example, 30\% of a quantity means \frac{30}{100} times the quantity); solve problems involving finding the whole, given a part and the percent.

How to find the percent of a number

In order to find the percent of a number with or without a calculator:

  1. Identify the percent and consider if there is a simple equivalent fraction.
  2. Decide which method to use.
  3. Work out the answer.

[FREE] Percents Check for Understanding Quiz (Grade 6 to 7)

[FREE] Percents Check for Understanding Quiz (Grade 6 to 7)

[FREE] Percents Check for Understanding Quiz (Grade 6 to 7)

Use this quiz to check your grade 6 to 7 students’ understanding of percents. 10+ questions with answers covering a range of 6th and 7th grade percent topics to identify areas of strength and support!

DOWNLOAD FREE
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[FREE] Percents Check for Understanding Quiz (Grade 6 to 7)

[FREE] Percents Check for Understanding Quiz (Grade 6 to 7)

[FREE] Percents Check for Understanding Quiz (Grade 6 to 7)

Use this quiz to check your grade 6 to 7 students’ understanding of percents. 10+ questions with answers covering a range of 6th and 7th grade percent topics to identify areas of strength and support!

DOWNLOAD FREE

Percent of a number examples

Example 1: simple percent without a calculator

Find 75\% of 120 \ km.

  1. Identify the percent and consider if there is a simple equivalent fraction.

75 \%=\cfrac{75}{100}=\cfrac{3}{4}

2Decide which method to use.

You can use 75\% as a fraction to solve or, since 75\% is easily related to 25\% and 50\% , you can use ratios to solve.

3Work out the answer.

Start with 120, which is the whole, or 100\%, and work down the table using ratios.

Percent of a Number example 1

Now use the ratios in the table to find 75\%.

75\% = 50\% + 25\%, so 75\% = 60 + 30.

75\% of 120 is 90.

Example 2: simple percent without a calculator

Find 10\% of 450 \ kg.

Identify the percent and consider if there is a simple equivalent fraction.

Decide which method to use.

Work out the answer.

Example 3: percent decomposed to 10% and 1%

Find 16\% of \$300.

Identify the percent and consider if there is a simple equivalent fraction.

Decide which method to use.

Work out the answer.

Example 4: the 1% method

Find 23\% of 700.

Identify the percent and consider if there is a simple equivalent fraction.

Decide which method to use.

Work out the answer.

Example 5: decimal multiplier

Work out 78\% of \$411.

Identify the percent and consider if there is a simple equivalent fraction.

Decide which method to use.

Work out the answer.

Example 6: decimal multiplier

Work out 61\% of 728.

Identify the percent and consider if there is a simple equivalent fraction.

Decide which method to use.

Work out the answer.

Teaching tips for percent of a number

  • Worksheets have their place for learning how to find the percent of a number, but they also ensure that students have plenty of opportunities to share their thinking with others. As this page outlines, there are many different ways to go about solving percentage problems, which means there are many opportunities for students to talk and think critically about their work and the work of others.

  • There are many different real world situations that students can connect to when learning this topic, such as finding the sales tax on an original price or calculating the sale price based on a percentage decrease.

  • Give students time to specifically look for patterns with a calculator as they find different percents of the same number. Ask questions like, “How do you notice the decimal places changing?” or “What do you notice about the percent of a number and the original number?” to encourage student thinking.

  • Once students have a foundational understanding of this topic and can flexibly move between strategies, it is okay to let them use a percentage calculator or other online calculators that do the calculations for them. This allows students to shift their focus to more complicated word problems or real-world application for percent of a number.

Easy mistakes to make

  • Incorrectly converting from a percent to a decimal
    When a percent is represented with a percent symbol, to convert it to a decimal you must divide by 100 (which is the same as moving the decimal point two places to the left) before multiplying.
    For example,
    What is 53\% of 200?
    US Percent of a Number image 2US Percent of a Number image 3

  • Adding or subtracting the same thing in a ratio table
    A ratio table can be used to represent the multiplicative relationship between a number and a percent of that number. Adding or subtracting the same thing from both sides does not preserve that relationship.
    For example,

    Percent of a Number image 4Percent of a Number image 5US Percent of a Number image 6US Percent of a Number image 7

  • Making calculation mistakes when multiplying by a fraction or dividing by a whole number
    It is a good idea to always check your work after solving (with or without a calculator). A good way to do this is to consider what a reasonable answer should be.
    For example,
    What is 11\% of 220?
    Before solving, notice that 11\% is close to 10\% and 10\% of a number is like dividing by 10 or moving the decimal to the left once, so the answer should be close to 22. If you get an answer that is much smaller or larger than 22, it most likely means you made a mistake calculating and you should check your work.

  • Not filling both decimal positions for a money answer
    For example, an answer of \$16.5 should be written as \$16.50. There are two digits needed to include the penny position.

Percent of a number practice questions

1. Find 25\% of \$280 without a calculator.

\$140
GCSE Quiz False

\$28
GCSE Quiz False

\$240
GCSE Quiz False

\$70
GCSE Quiz True

25\% is easily related to 100\% and 50\%, so you can use ratios to solve.

 

Start with 280, which is the whole, or 100\%, and work down the table using ratios.

 

Percent of a Number practice question 1

 

25\% of \$280 is \$70.

2. Find 50\% of 70 \, kg without a calculator.

35 \, kg
GCSE Quiz True

7 \, kg
GCSE Quiz False

17.5 \, kg
GCSE Quiz False

50 \, kg
GCSE Quiz False
50 \%=\cfrac{50}{100}=\cfrac{25}{50}=\cfrac{5}{10}=\cfrac{1}{2}

 

\cfrac{1}{2} \, is the simplest fraction for 50\%, so it will be the easiest to solve with.

 

So you can calculate…

 

\$ 70 \times \cfrac{1}{2}=\cfrac{\$ 70}{2}=\$ 35

 

OR

 

\$ 70 \div 2=\$ 35

3. Find 12\% of 200 \, g without a calculator.

40 \, g
GCSE Quiz False

24 \, g
GCSE Quiz True

16.67 \, g
GCSE Quiz False

25 \, g
GCSE Quiz False

10\% of 200 :

 

200 \div 10 = 20

 

1\% of 200 :

 

200 \div 100 = 2

 

\begin{aligned} 12\%&=10\%+(2 \times 1\%)\\\\ &=20+(2 \times 2)\\\\ &=24 \end{aligned}

4. Find 27\% of 300 \, km without a calculator.

75 \, km
GCSE Quiz False

81 \, km
GCSE Quiz True

67 \, km
GCSE Quiz False

27 \, km
GCSE Quiz False

10\% of 300 \, km :

 

300 \div 10 = 30

 

1\% of 300 \, km :

 

300 \div 100 = 3

 

\begin{aligned} 27\%&=(2 \times 10\%) + (7 \times 1\%)\\\\ &=(2 \times 30) + (7 \times 3)\\\\ &=60+21\\\\ &=81 \, km \end{aligned}

5. Find 57\% of \$710 with a calculator.

\$404.70
GCSE Quiz True

\$404.07
GCSE Quiz False

\$12.46
GCSE Quiz False

\$570
GCSE Quiz False

Convert the percent to a decimal, then multiply.

 

57\%=\cfrac{57}{100} = 0.57

 

\$710 \times 0.57 = \$404.70

6. Find 83\% of \$179 with a calculator.

\$30.43
GCSE Quiz False

\$83.79
GCSE Quiz False

\$148.57
GCSE Quiz True

\$143.20
GCSE Quiz False

Convert the percent to a decimal, then multiply.

 

83\%=\cfrac{83}{100}=0.83

 

\$179 \times 0.83 = \$148.57

Percent of a number FAQs

How do you write a percent in decimal form and fraction form?

A percent is a ratio out of 100, so the denominator of the fraction is always 100 , and the numerator is the percent written as a whole number. To convert this to a decimal, write the percent as a decimal ending in the hundredths column. Note this is true for whole number percents only.

Why is a percent always out of \bf{100} ?

In our number system, percents are a special type of ratio and we use 100 to represent the whole. The word percent broken up is per-cent, per representing a ratio and ‘cent’ meaning 100, like in the word century or 100 cents in a dollar.

Still stuck?

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