Ratios & Proportional Relationships

Ratios Comparison of two numbers by division. Ratios can compare parts of a whole or compare one part to the whole. Can be written three ways: –Fraction –Colon –“To”

Ratios-Example Write a ratio of squares to triangles ¾ 3:4 3 to 4

Rate A ratio that compares two numbers that have different units Example: –12 pencils 4 notebooks

Equivalent Ratios Equivalent ratios have different numbers but represent the same relationship. Similar to equivalent fractions

How to Find Equivalent Ratios Multiply or divide the numerator and denominator by the same number

Unit Rate A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

How to Find Unit Rate Divide the numerator and denominator by the number in the denominator

Percent A percent is a ratio that compares a number to 100. It represents part of a whole. Shaded 54 = 54% Total 100

Percents, Fractions & Decimals Since percents, fractions and decimals you can convert between the three

How to Change Percents to Decimals & Fractions To Change a Percent to a Decimal Move the decimal 2 places left (divide by 100) 75% = 0.75 To Change a Percent to a Fraction Put the number over 100 and put in simplest form 75 = = 4

How to Change Fractions & Decimals into Percents To Change a Decimal to a Percent Move the decimal 2 places right (multiply by 100) 0.45 = 45 % To Change a Fraction to a Percent Divide numerator by denominator Move the decimal 2 places right 3/8 = = 37.5%

How to Find the Percent of a Number Change the percent to a decimal Multiply the decimal by the number Example: Find 90% of 30 –Change 90% to decimal 0.90 –0.90 x 30 = 27 –So 90% of 30 is 27

How to Find Whole from a Percent You can use equivalent ratios to find the whole, given a part and the percent –Put the percent over 100 –Put 54 over an unknown –Use cross multiplication to solve Example: 54 is 60% of what number? –60 = ?