Proportions Explained: Definition, Examples, Practice & Video Lessons

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Concept

Intro To Proportions

Video duration:

2m

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Problem

Express the sentence as a proportion.
Ten is to fifteen as four is to six.

A

$\frac{10}{15} = \frac{6}{4}$

B

$\frac{10}{15} = \frac{4}{6}$

C

$\frac{10}{4}\)=\(\frac{15}{6}$

D

$$\frac{15}{10}$=$\frac$46$

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Problem

Express the sentence as a proportion.
Two thirds is to one fifth as two fifths is to one ninth.

A

$\frac{\frac{2}{3}}{\frac{1}{5}} = \frac{\frac{1}{9}}{\frac{2}{5}}$

B

$\frac{\frac{2}{5}}{\frac{1}{9}} = \frac{\frac{2}{3}}{\frac{1}{5}}$

C

$\frac{2}{3} = \frac{1}{5} = \frac{2}{5} = \frac{1}{9}$

D

$\frac{\frac{2}{3}}{\frac{1}{5}} = \frac{\frac{2}{5}}{\frac{1}{9}}$

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Problem

Express the sentence as a proportion.
A recipe uses 3 cups of rice for 5 cups of broth, and 15 cups of rice for 25 cups of broth.

A

$\frac{3 c . r i c e}{5 c . b r o t h} = \frac{25 c . r i c e}{15 c . b r o t h}$

B

$\frac{3 c . r i c e}{15 c . b r o t h} = \frac{5 c . r i c e}{25 c . b r o t h}$

C

$\frac{3 c . r i c e}{5 c . b r o t h} = \frac{15 c . r i c e}{25 c . b r o t h}$

D

$$\frac{15c.rice}{5c.bro\operatorname{\mathrm{th}$}}=$\frac{25c.rice}{3c.bro\operatorname{\mathrm{th}$}}$

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Problem

Express the sentence as a proportion.
A car travels 80 miles in 2 hours and 120 miles in 3 hours.

A

$\frac{80 m i}{2 h r s} = \frac{120 m i}{3 h r s}$

B

$\frac{80 m i}{3 h r s} = \frac{120 m i}{2 h r s}$

C

$\frac{2 m i}{80 h r s} = \frac{3 m i}{120 h r s}$

D

$\frac{80 m i}{120 h r s} = \frac{2 m i}{3 h r s}$

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Problem

Express the sentence as a proportion.
A paint mixture uses 2.5 liters of blue paint for every 4 liters of white paint, and another mixture uses 7.5 liters of blue paint for every 12 liters of white paint.

A

$\frac{2.5 L b l u e}{12 L w h i t e} = \frac{7.5 L b l u e}{4 L w h i t e}$

B

$\frac{2.5 L b l u e}{4 L w h i t e} = \frac{7.5 L b l u e}{12 L w h i t e}$

C

$$\frac{4\operatorname{\mathrm{L}$}blue}{2.5$\operatorname{\mathrm{L}$}white}=$\frac{12\operatorname{\mathrm{L}$}blue}{7.5$\operatorname{\mathrm{L}$}white}$

D

$$\frac{2.5\operatorname{\mathrm{L}$}blue}{7.5$\operatorname{\mathrm{L}$}white}=$\frac{4\operatorname{\mathrm{L}$}blue}{12$\operatorname{\mathrm{L}$}white}$

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Problem

Express the sentence as a proportion.
A trail map shows 3.6 miles in 1.2 hours, while another section shows 7 miles in $2 and one third$ hours.

A

$\frac{3.6 m i}{2 \frac{1}{3} h r s} = \frac{7 m i}{1.2 h r s}$

B

$\frac{1.2 m i}{3.6 h r s} = \frac{2 \frac{1}{3} m i}{7 h r s}$

C

$\frac{3.6 m i}{7 h r s} = \frac{1.2m i}{2 \frac{1}{3} h r s}$

D

A

$\frac{1 \frac{8}{10}}{2} = \frac{4 \frac{5}{10}}{5}$ ; False

B

$\frac{2}{1 \frac{8}{10}} = \frac{5}{4 \frac{5}{10}}$ ; True

C

$\frac{1 \frac{8}{10}}{2} = \frac{4 \frac{5}{10}}{5}$ ; True

D

$$\frac{2}{1\frac{8}{10}$}=$\frac{5}{4\frac{5}{10}$}$ ; False

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Problem

Write the sentence as a proportion then determine whether the proportion is true or false.
Four bags of flour costs \$12, and eight bags of flour costs \$18.

A

$\frac{4}{12} = \frac{8}{18}$ ; True

B

$\frac{4}{12} = \frac{8}{16}$ ; True

C

Video duration:

2m

Proportions: Videos & Practice Problems

Intro To Proportions

Express the sentence as a proportion.
Ten is to fifteen as four is to six.

Express the sentence as a proportion.
Two thirds is to one fifth as two fifths is to one ninth.

Express the sentence as a proportion.
A recipe uses 3 cups of rice for 5 cups of broth, and 15 cups of rice for 25 cups of broth.

Express the sentence as a proportion.
A car travels 80 miles in 2 hours and 120 miles in 3 hours.

Express the sentence as a proportion.
A paint mixture uses 2.5 liters of blue paint for every 4 liters of white paint, and another mixture uses 7.5 liters of blue paint for every 12 liters of white paint.

Express the sentence as a proportion.
A trail map shows 3.6 miles in 1.2 hours, while another section shows 7 miles in $2 and one third$ hours.

Determine If Proportions Are True

Determine whether the proportion is true or false.
$\frac{1 \frac{2}{3}}{3} = \frac{3 \frac{1}{3}}{6}$

Determine whether the proportion is true or false.
$\frac{2.4}{6} = \frac{1.2}{4}$

Use cross products to determine whether the proportion is true or false.
$\frac{7}{4} = \frac{20}{12}$

Use cross products to determine whether the proportion is true or false.
$\frac{4}{9} = \frac{12}{27}$

Write the sentence as a proportion then determine whether the proportion is true or false.
One and eight tenths is to two as four and five tenths is to five.

Write the sentence as a proportion then determine whether the proportion is true or false.
Four bags of flour costs \$12, and eight bags of flour costs \$18.

Solving Proportions

Solve the proportion using cross products.
$\frac{5}{8} = \frac{k}{24}$

Solve the proportion using cross products.
$\frac{2.5}{5} = \frac{p}{12}$

Solve the proportion using cross products.
$\frac{\frac{1}{3}}{\frac{3}{8}} = \frac{\frac{2}{5}}{n}$

Solving Proportions Example 1

Your Prealgebra & Beginning Algebra tutors

Proportions: Videos & Practice Problems

Intro To Proportions

Express the sentence as a proportion.Ten is to fifteen as four is to six.

Express the sentence as a proportion.Two thirds is to one fifth as two fifths is to one ninth.

Express the sentence as a proportion.A recipe uses 3 cups of rice for 5 cups of broth, and 15 cups of rice for 25 cups of broth.

Express the sentence as a proportion.A car travels 80 miles in 2 hours and 120 miles in 3 hours.

Express the sentence as a proportion.A paint mixture uses 2.5 liters of blue paint for every 4 liters of white paint, and another mixture uses 7.5 liters of blue paint for every 12 liters of white paint.

Express the sentence as a proportion.A trail map shows 3.6 miles in 1.2 hours, while another section shows 7 miles in 2132\(\frac\)13 hours.

Determine If Proportions Are True

Determine whether the proportion is true or false.1233=3136\(\frac{1\frac23}{3}\)=\(\frac{3\frac13}{6}\)

Determine whether the proportion is true or false.2.46=1.24\(\frac{2.4}{6}\)=\(\frac{1.2}{4}\)

Use cross products to determine whether the proportion is true or false.74=2012\(\frac\)74=\(\frac{20}{12}\)

Use cross products to determine whether the proportion is true or false.49=1227\(\frac\)49=\(\frac{12}{27}\)

Write the sentence as a proportion then determine whether the proportion is true or false.One and eight tenths is to two as four and five tenths is to five.

Write the sentence as a proportion then determine whether the proportion is true or false.Four bags of flour costs \$12, and eight bags of flour costs \$18.

Solving Proportions

Solve the proportion using cross products.58=k24\(\frac\)58=\(\frac{k}{24}\)

Solve the proportion using cross products.2.55=p12\(\frac{2.5}{5}\)=\(\frac{p}{12}\)

Solve the proportion using cross products.1338=25n\(\frac{\frac13}{\frac38}\)=\(\frac{\frac25}{n}\)

Solving Proportions Example 1

Your Prealgebra & Beginning Algebra tutors

Express the sentence as a proportion.
Ten is to fifteen as four is to six.

Express the sentence as a proportion.
Two thirds is to one fifth as two fifths is to one ninth.

Express the sentence as a proportion.
A recipe uses 3 cups of rice for 5 cups of broth, and 15 cups of rice for 25 cups of broth.

Express the sentence as a proportion.
A car travels 80 miles in 2 hours and 120 miles in 3 hours.

Express the sentence as a proportion.
A paint mixture uses 2.5 liters of blue paint for every 4 liters of white paint, and another mixture uses 7.5 liters of blue paint for every 12 liters of white paint.

Express the sentence as a proportion.
A trail map shows 3.6 miles in 1.2 hours, while another section shows 7 miles in $2 and one third$ hours.

Determine whether the proportion is true or false.
$\frac{1 \frac{2}{3}}{3} = \frac{3 \frac{1}{3}}{6}$

Determine whether the proportion is true or false.
$\frac{2.4}{6} = \frac{1.2}{4}$

Use cross products to determine whether the proportion is true or false.
$\frac{7}{4} = \frac{20}{12}$

Use cross products to determine whether the proportion is true or false.
$\frac{4}{9} = \frac{12}{27}$

Write the sentence as a proportion then determine whether the proportion is true or false.
One and eight tenths is to two as four and five tenths is to five.

Write the sentence as a proportion then determine whether the proportion is true or false.
Four bags of flour costs \$12, and eight bags of flour costs \$18.

Solve the proportion using cross products.
$\frac{5}{8} = \frac{k}{24}$

Solve the proportion using cross products.
$\frac{2.5}{5} = \frac{p}{12}$

Solve the proportion using cross products.
$\frac{\frac{1}{3}}{\frac{3}{8}} = \frac{\frac{2}{5}}{n}$