7th Grade Math Worksheets, Math Worksheets for Grade 7

1. Question

Match the following expressions with their respective values.

6 $\frac{1}{12}$
4 $\frac{7}{8}$
9 $\frac{12}{21}$

2 $\frac{5}{21}$ + 7 $\frac{1}{3}$
2 $\frac{7}{12}$ + 3 $\frac{2}{4}$
3 $\frac{2}{4}$ + 1 $\frac{3}{8}$

IMPRESSIVE!

EXPLANATION

i. 2 $\frac{5}{21}$ + 7 $\frac{1}{3}$

= $\frac{2 × 21 + 5}{21}$ + $\frac{7 × 3 + 1}{3}$	[Convert into improper fractions]
= $\frac{47}{21}$ + $\frac{22}{3}$
= $\frac{47}{21}$ + $\frac{22 × 7}{3 × 7}$	[Write equivalent fractions]
= $\frac{47}{21}$ + $\frac{154}{21}$
= $\frac{47 + 154}{21}$	[Add]
= $\frac{201}{21}$	[Simplify]
= 9 $\frac{12}{21}$	[Write as a mixed fraction]

ii. 2 $\frac{7}{12}$ + 3 $\frac{2}{4}$

= $\frac{2 × 12 + 7}{12}$ + $\frac{3 × 4 + 2}{4}$	[Convert into improper fractions]
= $\frac{31}{12}$ + $\frac{14}{4}$
= $\frac{31}{12}$ + $\frac{14 × 3}{4 × 3}$	[Write equivalent fractions]
= $\frac{31}{12}$ + $\frac{42}{12}$
= $\frac{31 + 42}{12}$	[Add]
= $\frac{73}{12}$	[Simplify]
= 6 $\frac{1}{12}$	[Write as a mixed fraction]

iii. 3 $\frac{2}{4}$ + 1 $\frac{3}{8}$

= $\frac{3 × 4 + 2}{4}$ + $\frac{1 × 8 + 3}{8}$	[Convert into improper fractions]
= $\frac{14}{4}$ + $\frac{11}{8}$
= $\frac{14 × 2}{4 × 2}$ + $\frac{11}{8}$	[Write equivalent fractions]
= $\frac{28}{8}$ + $\frac{11}{8}$
= $\frac{28 + 11}{8}$	[Add]
= $\frac{39}{8}$	[Simplify]
= 4 $\frac{7}{8}$	[Write as a mixed fraction]

KEEP LEARNING!

EXPLANATION

i. 2 $\frac{5}{21}$ + 7 $\frac{1}{3}$

= $\frac{2 × 21 + 5}{21}$ + $\frac{7 × 3 + 1}{3}$	[Convert into improper fractions]
= $\frac{47}{21}$ + $\frac{22}{3}$
= $\frac{47}{21}$ + $\frac{22 × 7}{3 × 7}$	[Write equivalent fractions]
= $\frac{47}{21}$ + $\frac{154}{21}$
= $\frac{47 + 154}{21}$	[Add]
= $\frac{201}{21}$	[Simplify]
= 9 $\frac{12}{21}$	[Write as a mixed fraction]

ii. 2 $\frac{7}{12}$ + 3 $\frac{2}{4}$

= $\frac{2 × 12 + 7}{12}$ + $\frac{3 × 4 + 2}{4}$	[Convert into improper fractions]
= $\frac{31}{12}$ + $\frac{14}{4}$
= $\frac{31}{12}$ + $\frac{14 × 3}{4 × 3}$	[Write equivalent fractions]
= $\frac{31}{12}$ + $\frac{42}{12}$
= $\frac{31 + 42}{12}$	[Add]
= $\frac{73}{12}$	[Simplify]
= 6 $\frac{1}{12}$	[Write as a mixed fraction]

iii. 3 $\frac{2}{4}$ + 1 $\frac{3}{8}$

= $\frac{3 × 4 + 2}{4}$ + $\frac{1 × 8 + 3}{8}$	[Convert into improper fractions]
= $\frac{14}{4}$ + $\frac{11}{8}$
= $\frac{14 × 2}{4 × 2}$ + $\frac{11}{8}$	[Write equivalent fractions]
= $\frac{28}{8}$ + $\frac{11}{8}$
= $\frac{28 + 11}{8}$	[Add]
= $\frac{39}{8}$	[Simplify]
= 4 $\frac{7}{8}$	[Write as a mixed fraction]

2. Question

Select the correct statement(s) for the given mixed numbers.
A = 1 $\frac{1}{3}$ , B = 1 $\frac{4}{6}$ , and C = 2 $\frac{2}{3}$ .

Statement 1: The sum of A and B is 3.
Statement 2: The sum of A and C is 4.

1.
Statement 2 is correct.
2.
Statement 1 is correct.
3.
Statement 2 is incorrect.
4.
Statement 1 is incorrect.

YIPPEE… YOU GOT IT RIGHT!

EXPLANATION

Let's check statement 1:

= 1 $\frac{1}{3}$ + 1 $\frac{4}{6}$
= $\frac{1 × 3 + 1}{3}$ + $\frac{ 1 × 6 + 4}{6}$	[Convert into mixed fractions]
= $\frac{4}{3}$ + $\frac{10}{6}$	[Add]
= $\frac{4 × 2}{3 × 2}$ + $\frac{10}{6}$	[Writing as an equivalent fractions]
= $\frac{8}{6}$ + $\frac{10}{6}$
= $\frac{8 + 10}{6}$	[Adding both the fractions]
= $\frac{18}{6}$	[Simplify]
= 3	[Result]

So, statement 1 is correct.

Now, let's check statement 2:

= 1 $\frac{1}{3}$ + 2 $\frac{2}{3}$
= $\frac{1 × 3 + 1}{3}$ + $\frac{2 ×3 + 2}{3}$	[Convert into improper fractions]
= $\frac{4}{3}$ + $\frac{8}{3}$	[Add]
= $\frac{4 + 8}{3}$	[Add the fractions]
= $\frac{12}{3}$
= 4	[Result]

So, statement 2 is correct.

So, both the statements are correct.

THERE’S ALWAYS A NEXT TIME!

EXPLANATION

Let's check statement 1:

= 1 $\frac{1}{3}$ + 1 $\frac{4}{6}$
= $\frac{1 × 3 + 1}{3}$ + $\frac{ 1 × 6 + 4}{6}$	[Convert into mixed fractions]
= $\frac{4}{3}$ + $\frac{10}{6}$	[Add]
= $\frac{4 × 2}{3 × 2}$ + $\frac{10}{6}$	[Writing as an equivalent fractions]
= $\frac{8}{6}$ + $\frac{10}{6}$
= $\frac{8 + 10}{6}$	[Adding both the fractions]
= $\frac{18}{6}$	[Simplify]
= 3	[Result]

So, statement 1 is correct.

Now, let's check statement 2:

= 1 $\frac{1}{3}$ + 2 $\frac{2}{3}$
= $\frac{1 × 3 + 1}{3}$ + $\frac{2 ×3 + 2}{3}$	[Convert into improper fractions]
= $\frac{4}{3}$ + $\frac{8}{3}$	[Add]
= $\frac{4 + 8}{3}$	[Add the fractions]
= $\frac{12}{3}$
= 4	[Result]

So, statement 2 is correct.

So, both the statements are correct.

3. Question

Harry joins two ropes of length 4 $\frac{3}{8}$ meters and 3 $\frac{1}{2}$ meters, and then cuts $\frac{21}{4}$ meters of rope. What is the remaining length of the rope?

1.
$\frac{21}{8}$
2.
$\frac{29}{8}$
3.
$\frac{21}{5}$
4.
$\frac{23}{8}$

WELL DONE! YOU GOT IT RIGHT.

EXPLANATION

Let's find the total length of the rope by adding the lengths of both the ropes.

= 4 $\frac{3}{8}$ + 3 $\frac{1}{2}$
= $\frac{8 × 4 + 3}{8}$ + $\frac{3 × 2 + 1}{2}$	[Convert into improper fractions]
= $\frac{32 + 3}{8}$ + $\frac{6+ 1}{2}$
= $\frac{35}{8}$ + $\frac{7}{2}$
= $\frac{35}{8}$ + $\frac{7 × 4}{2 × 4}$	[Write equivalent fractions]
= $\frac{35}{8}$ + $\frac{28}{8}$
= $\frac{35 + 28}{8}$	[Add]
= $\frac{63}{8}$	[Simplify]

So, total length of rope is $\frac{63}{8}$ meters.

It is mentioned that Harry cut $\frac{21}{4}$ m of rope.

Then,

= $\frac{63}{8}$ - $\frac{21}{4}$
= $\frac{63}{8}$ - $\frac{21 × 2}{4 × 2}$	[Write equivalent fractions]
= $\frac{63}{8}$ - $\frac{42}{8}$	[Subtract]
= $\frac{63 - 42}{8}$
= $\frac{21}{8}$	[Result]

Hence, the remaining length of the rope is $\frac{21}{8}$ meters.

GIVE IT ANOTHER TRY.

EXPLANATION

Let's find the total length of the rope by adding the lengths of both the ropes.

= 4 $\frac{3}{8}$ + 3 $\frac{1}{2}$
= $\frac{8 × 4 + 3}{8}$ + $\frac{3 × 2 + 1}{2}$	[Convert into improper fractions]
= $\frac{32 + 3}{8}$ + $\frac{6+ 1}{2}$
= $\frac{35}{8}$ + $\frac{7}{2}$
= $\frac{35}{8}$ + $\frac{7 × 4}{2 × 4}$	[Write equivalent fractions]
= $\frac{35}{8}$ + $\frac{28}{8}$
= $\frac{35 + 28}{8}$	[Add]
= $\frac{63}{8}$	[Simplify]

So, total length of rope is $\frac{63}{8}$ meters.

It is mentioned that Harry cut $\frac{21}{4}$ m of rope.

Then,

= $\frac{63}{8}$ - $\frac{21}{4}$
= $\frac{63}{8}$ - $\frac{21 × 2}{4 × 2}$	[Write equivalent fractions]
= $\frac{63}{8}$ - $\frac{42}{8}$	[Subtract]
= $\frac{63 - 42}{8}$
= $\frac{21}{8}$	[Result]

Hence, the remaining length of the rope is $\frac{21}{8}$ meters.

4. Question

What is the sum of 13 $\frac{1}{5}$ and 11 $\frac{2}{15}$ ?

1.
24 $\frac{1}{3}$
2.
14 $\frac{1}{3}$
3.
24 $\frac{11}{3}$
4.
24 $\frac{1}{5}$

FANTASTIC!

EXPLANATION

Let's add the whole part and the fractional part separately.

= 13 $\frac{1}{5}$ + 11 $\frac{2}{15}$
= (13 + 11) + $\frac{1 × 3}{5 × 3}$ + $\frac{2}{15}$	[Adding the whole number part and fraction part separately]
= 24 + $\frac{3 + 2}{15}$	[Add]
= 24 + $\frac{5}{15}$	[Simplify]
= 24 $\frac{1}{3}$	[Merge both the parts to get the mixed fraction]

Hence, 13 $\frac{1}{5}$ + 11 $\frac{2}{15}$ = 24 $\frac{1}{3}$

GO FURTHER, YOU CAN BE A CHAMP!

EXPLANATION

Let's add the whole part and the fractional part separately.

= 13 $\frac{1}{5}$ + 11 $\frac{2}{15}$
= (13 + 11) + $\frac{1 × 3}{5 × 3}$ + $\frac{2}{15}$	[Adding the whole number part and fraction part separately]
= 24 + $\frac{3 + 2}{15}$	[Add]
= 24 + $\frac{5}{15}$	[Simplify]
= 24 $\frac{1}{3}$	[Merge both the parts to get the mixed fraction]

Hence, 13 $\frac{1}{5}$ + 11 $\frac{2}{15}$ = 24 $\frac{1}{3}$

5. Question

Jenny buys 1 $\frac{4}{5}$ lb of cheese to make sandwiches. She uses 1 $\frac{3}{10}$ lb. How much cheese does Jenny have left?

1.
$\frac{5}{10}$
2.
$\frac{1}{2}$
3.
$\frac{1}{3}$
4.
$\frac{11}{2}$

A BUDDING MATHEMATICAL GENIUS AT WORK!

EXPLANATION

The total amount of cheese given = 1 $\frac{4}{5}$ lb
Cheese used for sandwiches = 1 $\frac{3}{10}$ lb

Then, amount of cheese left = 1 $\frac{4}{5}$ - 1 $\frac{3}{10}$

= $\frac{1 × 5 + 4}{5}$ - $\frac{1 × 10 + 3}{10}$	[Convert into improper fractions]
= $\frac{9}{5}$ - $\frac{13}{10}$	[Add]
= $\frac{9 × 2}{5 × 2}$ - $\frac{13}{10}$	[Write equivalent fractions]
= $\frac{18}{10}$ - $\frac{13}{10}$	[Subtract]
= $\frac{18 - 13}{10}$
= $\frac{5}{10}$ (or) $\frac{1}{2}$	[Simplify]

Hence, Jenny has left with $\frac{5}{10}$ lb or $\frac{1}{2}$ lb amount of cheese.

PLEASE TRY ONE MORE TIME.

EXPLANATION

The total amount of cheese given = 1 $\frac{4}{5}$ lb
Cheese used for sandwiches = 1 $\frac{3}{10}$ lb

Then, amount of cheese left = 1 $\frac{4}{5}$ - 1 $\frac{3}{10}$

= $\frac{1 × 5 + 4}{5}$ - $\frac{1 × 10 + 3}{10}$	[Convert into improper fractions]
= $\frac{9}{5}$ - $\frac{13}{10}$	[Add]
= $\frac{9 × 2}{5 × 2}$ - $\frac{13}{10}$	[Write equivalent fractions]
= $\frac{18}{10}$ - $\frac{13}{10}$	[Subtract]
= $\frac{18 - 13}{10}$
= $\frac{5}{10}$ (or) $\frac{1}{2}$	[Simplify]

Hence, Jenny has left with $\frac{5}{10}$ lb or $\frac{1}{2}$ lb amount of cheese.

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