# Arithmetic

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## Important Concepts in Arithmetic

Find notes, videos, important points and questions to practice on each of these concepts.

- Speed, Time and Distance
- Work
- Age
- Pipes and Cisterns

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## Important Points

A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8 and 12.

To compare ratios, write them as fractions. The ratios are equal if they are equal when written as fractions.

Remember to be careful! Order matters! A ratio of 1:7 is not the same as a ratio of 7:1.

A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. Four (non-zero) quantities of the same kind a, b, c, d are in proportion, written as a : b :: c : d if a/b = c/d

When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. Question marks or letters are frequently used in place of the unknown number.

To compare ratios, write them as fractions. The ratios are equal if they are equal when written as fractions.

Remember to be careful! Order matters! A ratio of 1:7 is not the same as a ratio of 7:1.

A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. Four (non-zero) quantities of the same kind a, b, c, d are in proportion, written as a : b :: c : d if a/b = c/d

When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. Question marks or letters are frequently used in place of the unknown number.