Ratio and Proportion Worksheets

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Ratios are pairs of numbers that say how much of one thing compares to another. They can be written in three different ways: with the word to, with a colon, or as a fraction.

See the fact file below for more information on Ratio and Proportions, or you can download our 22-page Ratio and Proportions worksheet pack to utilze within the classroom or home environment.

Key Facts & Information

RATIO AND PROPORTION

• The connection between the amounts of two or more items is defined by ratio. It is used to contrast portions of the same type.
• It is considered to be in proportion if two or more ratios are equal.
• There are two methods to display the proportion. It can be represented with either an equal sign or a colon symbol, as in a:b = c:d or a:b:: c:d.
• It does not affect the ratio whether we multiply or divide each term by the same number.
• If the ratio between the first and second amounts is identical to the ratio between the second and third quantities, the quantities are said to be in continuing proportion.

Ratio

• A ratio compares two quantities produced by dividing the first by the second. If a and b are two values of the same kind and with the same units, and b is not equal to zero, then the quotient a/b is known as the ratio between a and b. 
• The colon sign is used to denote ratios (:). The ratio a/b has no unit and may be expressed as a: b.

Proportion

• The equality of two ratios is referred to as proportion. Two equal ratios are always proportional. Proportions are represented by the symbol (::) and assist us in solving for unknown values. 
• The proportion is an equation or statement that shows that two ratios or fractions are comparable. 
• If a: b = c: d, four non-zero values, a, b, c, and d, are said to be in proportion. 
• Consider the ratios 10:20 and 250:500. In this case, 10:20 may be written as 10:20 = 10/20 = 0.5, and 250:500 can be written as 250:500 = 250/500 = 10/20 = 0.5. Because both ratios are equal, they are proportionate.
• Proportions are classified into three kinds.
  • Direct Proportion
  • Inverse Proportion
  • Continuous Proportion

Direct Proportion

• The term “direct proportion” refers to the link between two quantities. When one amount rises, the other rises, and vice versa. 
• As a result, a direct proportion is expressed as y∝x. For example, increasing the speed of an automobile causes it to travel more distance in a given amount of time.

Inverse Proportion

• Inverse proportion explains the connection between two quantities in which one rises while the other falls and vice versa. 
• As a result, an inverse proportion is expressed as y∝1/x. For example, when a vehicle’s speed increases, it will travel a constant distance in less time.

Continuous Proportion

• This refers to the relationship between three or more quantities where the ratio between each two consecutive terms is always the same. 
• To express the continuous proportion, you would not use the least common multiple of the means, but the common ratio, which is the ratio between the terms.
• For example, consider the following three ratios: a:b, b:c, and c:d. The common ratio is the ratio between consecutive terms, in this case, b:c. So the continuous proportion can be expressed as a:b:c:d or a:b=b:c=c:d. 
• The LCM of b and c for the given ratio is not used here.
• It’s important to note that in continuous proportion, we are not multiplying any of the terms, we are just expressing the proportionality between the terms in consecutive order.

FORMULA

• For example, the ratio 3: 2 can be written as 3/2, where 3 is the antecedent and 2 is the consequent.
• To indicate a proportion for the two ratios, a: b and c: d, we write them as a:b::c:d⟶a/b=c/d
• The terms b and c are known as mean terms.
• The terms a and d are referred to as extreme terms.
• In a: b = c: d, the values a and b must be of the same kind and have the same units, but c and d may be of the same type and have the same units independently. For example: 4 kg: 20 kg = Rs. 60: Rs. 300.
• The proportion formula is written as a/b = c/d or a: b:: c: d.
• The product of the means equals the outcome of the extremes in proportion. 
• As a result of the percentage formula a: b:: c: d, we obtain bxc = axd. For instance, in 4: 20: 60: 300, we get 4×20 = 60×300.

DIFFERENCE BETWEEN RATIO AND PROPORTION

• The following table shows the differences between ratio and proportion.

• You can compare any two amounts with the same units.
• Only if two ratios are equal are they considered to be in proportion.
• We may also use the cross-product approach to determine whether two ratios are equal and in proportion.
• The ratio stays the same whether we multiply and divide each term by the same number.
• If the ratio between the first and second amounts is identical to the ratio between the second and third, the quantities are said to be in a continuous proportion.
• Similarly, the ratio between the first and second items in a continuous proportion equals the ratio between the third and fourth.

Ratio and Proportion Worksheets

This is a fantastic bundle that includes everything you need to know about Ratio and Proportion across 22 in-depth pages. These are ready-to-use worksheets that are perfect for teaching students about Ratio and Proportion, mathematical concepts that describe the relationship between two or more values.

Complete List Of Included Worksheets

• Math: Ratio and Proportion Facts
• Word Play
• Applications
• What is the R&P
• Equivalent Ratios
• Mixed Jumbled Numbers
• On and Off
• Alt Sign
• Cross Multiplication
• Proportion Types
• Problem Solving

Frequently Asked Questions

What is the difference between ratio and proportion?

A ratio compares two or more quantities expressed as fractions or decimals. For example, the ratio of apples to bananas in a basket can be expressed as 3:2, meaning there are 3 apples for every 2 bananas.

A proportion, however, is an equation that states that two ratios are equal. For example, if the ratio of apples to bananas in a basket is 3:2, and there are 6 apples, then the proportion of apples to bananas would be 3/2 = 6/x, where x is the number of bananas. Solving for x, we can find that x = 4, so there are 4 bananas in the basket.

How do you solve a proportion?

To solve a proportion, you can use cross-multiplication. Cross-multiplication involves multiplying both sides of the proportion by the same value to isolate the unknown variable. For example, to solve the proportion 3/2 = 6/x, you can cross-multiply to get 3 * x = 2 * 6, and then divide both sides by 3 to get x = 4.

What is the meaning of the symbol “:” in a ratio?

The symbol “:” is used to express a ratio. For example, the ratio of apples to bananas in a basket can be written as 3:2, meaning there are 3 apples for every 2 bananas. The symbol “:” is read as “to” or “per”.

Can a ratio be expressed as a decimal or a percentage?

Yes, a ratio can be expressed as a decimal or a percentage. To convert a ratio to a decimal, you can divide the first number in the ratio by the second number. For example, the ratio 3:2 can be expressed as a decimal as 3/2 = 1.5. To convert a ratio to a percentage, you can multiply the decimal form of the ratio by 100. For example, 1.5 * 100 = 150, so the ratio 3:2 can be expressed as a percentage as 150%.

How do you find the ratio of two quantities?

To find the ratio of two quantities, you must divide the first quantity by the second. For example, if you have 6 apples and 4 bananas, you can find the ratio of apples to bananas as 6/4 = 3/2. The ratio of apples to bananas is 3:2, meaning there are 3 apples for every 2 bananas.

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Link will appear as Ratio and Proportion Worksheets: https://kidskonnect.com - KidsKonnect, June 29, 2023