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Ratios & Proportional Relationships
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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”
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Ratios-Example Write a ratio of squares to triangles ¾ 3:4 3 to 4
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Rate A ratio that compares two numbers that have different units Example: –12 pencils 4 notebooks
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Equivalent Ratios Equivalent ratios have different numbers but represent the same relationship. Similar to equivalent fractions
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How to Find Equivalent Ratios Multiply or divide the numerator and denominator by the same number
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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.
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How to Find Unit Rate Divide the numerator and denominator by the number in the denominator
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Percent A percent is a ratio that compares a number to 100. It represents part of a whole. Shaded 54 = 54% Total 100
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Percents, Fractions & Decimals Since percents, fractions and decimals you can convert between the three
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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 = 3 100 = 4
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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 = 0.375 = 37.5%
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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
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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 = 54 100 ?
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