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B2.3 · Calculate benchmark percents mentally

Learn to calculate benchmark percents mentally through clear examples and targeted practice.

Ontario Grade 6 Mathematics

Number

Use familiar parts of a whole to find benchmark percents

A percent tells how many parts out of 100 are being described. A benchmark percent is a familiar percent that is useful for mental calculations. For example, 50% means one half, and 25% means one quarter. You can use the matching part of a number to find the percent amount. In this lesson, you will begin with equal groups, connect them to percents, and use mental calculations to find benchmark percents.

What you will learn

  • Explain that a percent describes parts out of 100.
  • Connect benchmark percents to familiar equal parts of a whole.
  • Calculate benchmark percents of whole numbers mentally.
  • Check whether a calculated amount makes sense.

Connect percents to equal parts

A whole is the complete amount you are considering. If a bag holds 80 tiles, all 80 tiles are the whole. A percent describes a part of that whole by using 100 equal parts as a reference.
A fraction names equal parts of a whole. For example, one half is one of two equal parts. One quarter is one of four equal parts. A percent can match one of these familiar parts: 50% is one half, and 25% is one quarter.
Think about a strip divided into four equal boxes. If each box stands for the same number of tiles, one box is one quarter of all the tiles. The picture is a model: its four parts are equal, and one part represents 25% of the whole.
The number after the word “of” tells you which whole to use. So 25% of 92 means one quarter of 92. It does not mean one quarter of 100. Before you calculate, name the whole and match the percent to a familiar part.
50%=1250\% = \frac{1}{2}
  • A whole is the complete amount being considered.
  • A percent describes parts of a whole using 100 equal parts as a reference.
  • 50% is one half; 25% is one quarter.

Use benchmark percents to calculate mentally

A mental calculation is a calculation you can work out in your head. To find a benchmark percent, first match the percent to a familiar part. Then find that part of the whole.
To find 50% of a number, find half. For an even whole number, you can split it into two equal groups. For example, 50% of 86 is 43 because two groups of 43 make 86.
To find 25%, find one quarter: share the whole equally into four groups and find the amount in one group. To find 75%, find three quarters: calculate one quarter, then take three equal groups of that size.
Ten percent is one tenth of a number. One tenth means one of ten equal groups, so finding 10% means dividing the whole by 10. One percent is one hundredth of a number, so finding 1% means dividing the whole by 100. Choose whole numbers that make these parts easy to see mentally.
These are separate benchmark percents. Work out the part that matches the percent asked for. Do not treat an unrelated percent as a benchmark just because it can be built from other amounts.
25%=1425\% = \frac{1}{4}
  • Find the matching part of the whole: half, one quarter, or another familiar equal part.
  • 50% is half; 25% is one quarter; 75% is three quarters.
  • 10% is one tenth, and 1% is one hundredth.

Check the size of the answer

After calculating, compare the answer with the whole. For a benchmark less than 50%, the part should be less than half of the whole. For 50%, the part should be exactly half. For 75%, it should be more than half but less than the whole.
You can also check by rebuilding the whole from equal groups. If 25% of a number is 23, then four groups of 23 should make the original number. This check uses the same equal-part idea as the calculation.
For 10%, the amount should be one of ten equal groups. For 1%, it should be one of one hundred equal groups. Ask yourself whether the answer seems the right size for the whole. A quick size check can help catch a calculation mistake.
75%=3475\% = \frac{3}{4}
  • Compare the calculated part with the whole and with half of the whole.
  • Use equal groups to check that the part fits the benchmark.
  • A check does not replace the calculation; it helps you notice an answer that is too large or too small.

Try the steps yourself

When you meet a benchmark-percent question, use this simple routine: identify the whole, name the matching equal part, and calculate that part. Then check whether the result has the expected size.
For example, if the question asks for 25% of 92, the whole is 92. Since 25% is one quarter, split 92 into four equal groups. Each group has 23. Check by putting four groups of 23 back together: they make 92.
Keep the benchmark and the whole together in your thinking. One quarter of 92 is not the same amount as one quarter of a different whole. The percent tells which part to find; the number after “of” tells what to find it in.
  • Identify the whole before calculating.
  • Match the benchmark percent to equal parts.
  • Check your answer by rebuilding the whole or comparing sizes.

Worked example

Find 50% of 86

A collection has 86 cards. How many cards is 50% of the collection?
One half of 86 cards
One half of 86 cardsThe bar has two equal parts. One part is half of the collection and represents 43 cards.1/2 = 50%cards

The bar has two equal parts. One part is half of the collection and represents 43 cards.

  1. Match the benchmark
    Fifty percent means one half. So find half of the whole collection.
    50%=1250\% = \frac{1}{2}
  2. Split the whole equally
    Divide 86 cards into two equal groups. Each group has 43 cards, so one half of the collection is 43 cards.
    86÷2=4386 \div 2 = 43
Answer: 50% of 86 cards is 43 cards.
Check: Two groups of 43 make 86. The answer is exactly half of the collection.

Worked example

Find 25% of 92

A set has 92 counters. How many counters is 25% of the set?
One quarter of 92 counters
One quarter of 92 countersThe bar has four equal parts. One part represents 23 counters, or one quarter of the set.1/4 = 25%counters

The bar has four equal parts. One part represents 23 counters, or one quarter of the set.

  1. Match the percent to equal parts
    Twenty-five percent means one quarter. One quarter is one of four equal parts.
    25%=1425\% = \frac{1}{4}
  2. Find one equal part
    Share 92 counters equally into four groups. Each group has 23 counters, so one quarter of the set is 23 counters.
    92÷4=2392 \div 4 = 23
Answer: 25% of 92 counters is 23 counters.
Check: Four groups of 23 make 92. One group is one quarter of the set.

Worked example

Find 75% of 64

A box contains 64 tiles. How many tiles is 75% of the box?
Three quarters of 64 tiles
Three quarters of 64 tilesThe bar has four equal parts. Three of the four parts represent 48 tiles.3/4 = 75%tiles

The bar has four equal parts. Three of the four parts represent 48 tiles.

  1. Match the benchmark
    Seventy-five percent means three quarters. First find one quarter of the whole, then take three equal parts.
    75%=3475\% = \frac{3}{4}
  2. Find one quarter
    Share 64 tiles equally into four groups. Each group has 16 tiles.
    64÷4=1664 \div 4 = 16
  3. Take three equal parts
    Three groups of 16 contain 48 tiles. This is three quarters of the box.
    16+16+16=4816 + 16 + 16 = 48
Answer: 75% of 64 tiles is 48 tiles.
Check: Half of 64 is 32, and the whole is 64. The answer, 48, is between those amounts, as three quarters should be.

Common mistakes and how to avoid them

Finding the benchmark part of 100 instead of the number after “of.”
Correction: Use the number after “of” as the whole. For 25% of 92, find one quarter of 92.
Finding one quarter by splitting the whole into two groups.
Correction: One quarter means one of four equal groups. Split into four groups, not two.
Finding three quarters by taking only one quarter.
Correction: Find one quarter first, then take three equal groups of that size.
Accepting an answer that is larger than the whole when the benchmark is less than 100%.
Correction: A part that is less than the whole should be smaller than the whole. Compare the answer with the whole to check its size.

Lesson summary

  • A percent describes parts of a whole using 100 equal parts as a reference.
  • 50% means one half; 25% means one quarter; 75% means three quarters.
  • Find the matching equal part of the number after “of.”
  • Check your result by rebuilding the whole from equal groups or comparing its size with the whole.

Check your understanding

Question 1

What is 50% of 74?
  1. 37
  2. 24
  3. 148
  4. 7.4
Show answer and explanation
37
Fifty percent is one half. Half of 74 is 37.

Question 2

What is 25% of 68?
  1. 34
  2. 17
  3. 51
  4. 6.8
Show answer and explanation
17
Twenty-five percent is one quarter. One quarter of 68 is 17.

Question 3

What is 75% of 48?
  1. 12
  2. 24
  3. 36
  4. 40
Show answer and explanation
36
One quarter of 48 is 12. Three groups of 12 make 36, so 75% of 48 is 36.

Key terms

Percent
A way to describe parts of a whole using 100 equal parts as a reference.
Benchmark percent
A familiar percent that helps with a mental calculation, such as 25% or 50%.
Whole
The complete amount being considered.
Equal parts
Parts that have the same size or amount.

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