Recall common fraction, decimal, and percent equivalents

Ontario Grade 7 Mathematics

Number

Recall different names for the same amount

A strip is divided into four equal sections, and one section is shaded. The shaded amount has several familiar names: one quarter, 0.25, and 25%. These names look different, but they describe the same amount. This lesson focuses on recalling common matches and checking them with familiar examples. A fraction, a decimal, and a percent are different ways to write numbers. The percent sign means “out of one hundred.”

What you will learn

Recognize common fraction, decimal, and percent equivalents.
Recall an equivalent when given any one of its forms.
Use a simple visual comparison to check a familiar match.

Recognize equivalent names

Equivalent means having the same value. For example, one quarter and 25% are equivalent: each names the same amount of a whole. A decimal can name that amount too. So the complete match is one quarter, 0.25, and 25%.

A picture can help you recall a match. Imagine a bar split into four equal sections, with one section shaded. The shaded section is one quarter of the bar. If the same amount were shown as one hundred equal shares, 25 of them would represent that amount. The whole stays the same; only the way we name the amount changes.

The picture is a check, not a new list of rules. When two names are equivalent, they should describe the same amount. A quarter-sized part should not be matched with a name for half of a whole.

\frac{1}{4}=0.25=25\%

Equivalent forms name the same amount.
A percent describes an amount out of one hundred.
A visual model can help check a familiar match.

Build a small set of familiar matches

Some matches are especially useful to remember. One half matches 0.5 and 50%. One quarter matches 0.25 and 25%. Three quarters matches 0.75 and 75%. One whole matches 1, 1.0, and 100%.

A familiar match can help you recall another one. For example, three quarters is three quarter-sized parts, so it matches 0.75 and 75%. You can picture a bar with three of its four equal sections shaded. The shaded amount is more than half but less than the whole bar.

Use the table as a recall guide. Read each row across and say the three names aloud. Then cover one column and try to remember the missing names. The goal is to recognize the amount, not to treat each entry as an unrelated fact.

\frac{1}{2}=0.5=50\%

Remember common matches for one quarter, one half, three quarters, and one whole.
Use a familiar amount to help recall another form.
Practise recalling a match from different starting forms.

Check a match with a model

When a match seems unfamiliar, compare it with a simple picture or a match you already know. Start by identifying the whole shown. Then compare the amount in the picture with a familiar amount such as one half or one quarter.

For example, a bar divided into ten equal sections has seven shaded. The picture shows an amount commonly written as 0.7 and 70%. If the proposed match were 20%, it would not fit: the picture shows much more than one fifth of the bar. This kind of comparison helps catch a mismatch.

A model only works when its parts are equal. If sections have different sizes, counting sections alone can give a misleading picture of the amount. Use equal sections when checking a fraction model.

\frac{7}{10}=0.7=70\%

Compare the amount with a familiar match, such as one half or one quarter.
A model can help you spot a clearly incorrect match.
Use equal-sized sections in a fraction model.

Practise recalling in both directions

You may be given a fraction and asked to recall its decimal and percent, or you may be given a percent and asked to recall the other forms. Practise in both directions. For example, seeing 50% should bring to mind one half and 0.5.

If you are unsure, picture the matching amount and compare it with a familiar example. A picture of three shaded sections out of four is close to a whole, but not a whole. The familiar match is 0.75 and 75%.

Keep the forms together as you practise. Say or write the full set, then check that all three names describe the same amount. The table and examples in this lesson provide a short set of common equivalents to recall.

Practise starting with a fraction, decimal, or percent.
Use a picture or a familiar match as a check.
Keep all equivalent forms together when practising.

Common equivalents to recall

Fraction	Decimal	Percent
$\frac{1}{10}$	0.1	10%
$\frac{1}{5}$	0.2	20%
$\frac{1}{4}$	0.25	25%
$\frac{1}{2}$	0.5	50%
$\frac{3}{4}$	0.75	75%
$1$	1.0	100%

Worked example

Name a shaded quarter

A bar is split into four equal sections, and one section is shaded. Name the shaded amount as a fraction, decimal, and percent.

One quarter shaded

One of four equal sections is shaded. The bar represents one whole.

Recall the familiar amount
One shaded section out of four equal sections shows one quarter of the bar. This is a common equivalent set.
$\frac{1}{4}=0.25=25\%$
State the three names
The shaded amount can be named as a fraction, a decimal, or a percent. Each name describes the same part of the whole.
$\frac{1}{4},\ 0.25,\ 25\%$

Answer: The shaded amount is

\frac{1}{4}

, 0.25, or 25%.

Check: One quarter is less than one half. The matching 25% is also less than 50%.

Worked example

Start with a percent

A label shows 50%. What are the matching fraction and decimal?

One half shaded

One of two equal sections is shaded. The bar represents one whole.

Recall the familiar match
Fifty percent is a familiar name for one half of a whole.
$50\%=\frac{1}{2}$
Include the decimal
The decimal commonly paired with one half is 0.5. All three forms name the same amount.
$\frac{1}{2}=0.5=50\%$

Answer: The matching fraction is

\frac{1}{2}

, and the matching decimal is 0.5.

Check: One half and 50% both name half of a whole.

Worked example

Check a three-quarter match

A learner writes that

\frac{3}{4}

, 0.75, and 75% are equivalent. Is the match correct?

Three quarters shaded

Three of four equal sections are shaded. The bar represents one whole.

Recall the common set
Three quarters is a familiar amount. Its decimal and percent forms are 0.75 and 75%.
$\frac{3}{4}=0.75=75\%$
Compare the amounts
The picture shows three of four equal sections shaded. That is more than half of the whole but less than the whole, which fits 75%.
$50\%<75\%<100\%$

Answer: Yes. The three forms are equivalent.

Check: Three quarters is greater than one half and less than one whole, matching the comparison of 75% with 50% and 100%.

Common mistakes and how to avoid them

Pairing different names that do not describe the same amount.

Correction: Check the proposed names against a familiar match or a simple equal-section picture.

Thinking 0.5 and 50% describe different amounts because they look different.

Correction: They are common equivalent names for one half.

Using unequal sections in a fraction picture and comparing only the number of sections.

Correction: Use equal-sized sections so the picture represents the amount fairly.

Lesson summary

Equivalent fraction, decimal, and percent forms name the same amount.
Common matches include $\frac{1}{4}=0.25=25\%$ , $\frac{1}{2}=0.5=50\%$ , and $\frac{3}{4}=0.75=75\%$ .
Use familiar matches and equal-section pictures to check your recall.

Check your understanding

Question 1

Which set names the same amount?

$\frac{1}{4}$ , 0.25, 25%
$\frac{1}{4}$ , 0.5, 25%
$\frac{1}{2}$ , 0.25, 50%
$\frac{3}{4}$ , 0.25, 75%

Show answer and explanation

\frac{1}{4}

, 0.25, 25%

One quarter, 0.25, and 25% are common equivalent names.

Question 2

What fraction and decimal match 75%?

$\frac{1}{4}$ and 0.25
$\frac{3}{4}$ and 0.75
$\frac{1}{2}$ and 0.5
$\frac{1}{5}$ and 0.2

Show answer and explanation

\frac{3}{4}

and 0.75

Three quarters is the familiar fraction match for 75%, and 0.75 is its decimal match.

Key terms

Equivalent: Having the same value, even when written in different forms.
Percent: A way to name an amount out of one hundred.
Whole: The complete item or group being considered.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation B2.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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B2.2 · Recall common fraction, decimal, and percent equivalents

Ontario Grade 7 Mathematics

Recall different names for the same amount

What you will learn

Recognize equivalent names

Build a small set of familiar matches

Check a match with a model

Practise recalling in both directions

Common equivalents to recall

Name a shaded quarter

Start with a percent

Check a three-quarter match

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Key terms

Continue through Grade 7 Math

About this lesson and its review