Mental Mathematics

Grade 7: The Learning Equation Math

12.10 Mental Mathematics

Refresher pp 42-3

The student will:

convert mentally among fractions, decimals, and percents to facilitate the solution of problems.

Percent Review You can model percent with a 100 square grid. Click on the grey/red squares to increase/decrease the percent!! Remember a percent (%) can be written as fraction with a denominator of 100.
Percent	23 : 100 = 23% 32/100 = 32%	a ratio whose second term is 100. Percent means "parts per hundred". We use the symbol /100 or % for percent.
Converting Fractions to Percent	3/4 = 75/100 = 75% 2/5 = 40/100 = 40% 3/10 = 30/100 = 30% 9/25 = 36/100 = 36%	use equivalent fractions, if the denominator is a factor of 100. Algebra.help -- Fraction Simplifier
Converting Percent to Fractions	75% = 75/100 = 3/4 40% = 40/100 = 2/5 30% = 30/100 = 3/10 45% = 45/100 = 9/20	Change percent to a fraction with a denominatorof 100. Reduce to lowest terms. Quia - Matching - Percent - Fraction Match
Converting Fractions to Decimals	2/3 = 0.666... 15/9 = 1.555...	divide the numerator by the denominator if the denominator of the fraction is not a factor of 100. Algebra.help -- Fraction Simplifier Scientific Calculator
Converting Decimals to Fractions	0.84 = 84/100 = 21/25 1.43 = 1 43/100	Make sure there is at least two decimal places. Move the decimal to the end of the hundredth digit and then place this number over 100. Reduce to lowest terms. If there are more than two decimal places, then move the decimal to the end of the last digit, then place the number over the following denominators: 3 decimal places --> /1000 4 decimal places --> /10 000 Quia - Matching - Fraction Decimal Conversion
Converting Decimals to Fractions	0.333... = 3/9 0.666... = 6/9 = 2/3 1.555... = 1 5/9	For this course, the limit is single-digit nonterminating decimals. The denominator for these fractions is 9. Reduce to lowest terms. Quia - Concentration - Fraction Decimal Conversion
Converting Decimals to Percent	0.005 = 0.5% 0.23 = 23% 0.67 = 67% 2.17 = 217% 3.456 = 345.6%	multiply the decimal by 100 to change the decimal to a percent.
Converting Percent to Decimals	0.5% = 0.005 23% = 0.23 67% = 0.67 217% = 2.17 345.6% = 3.456	divide the percent by 100 to change the percent to a decimal

Estimating Percents

Estimating Percent - visual and interactive

10% Relationships

1% Relationships

A store is offering a 30% discount on pants. If the regular price for a pair of pants is $49.99, how much discount will you get?

10% Estimate: 10% of $50 is $5

30% Estimate: The discount will be about $15.

A pizza place is offering a7% discount on medium pizza.. If the regular price for the pizza is $9.99, how much discount will you get?

1% Estimate: 1% of $10 is $0.10

70% Estimate: The discount will be about $0.70

It is worth memorizing the most common fraction to decimal to percent conversions.

(tenth)	50%	33.3%	25%	20%	16.7%	12.5%	11%	10%	8.3%	6.7%	5%
(thousandth)	0.5	0.333	0.25	0.2	0.167	0.125	0.11	0.1	0.083	0.067	0.05
	1/2	1/3	1/4	1/5	1/6	1/8	1/9	1/10	1/12	1/15	1/20

Fraction/Decimal Conversion

Calculator Enter a fraction on the right hand side. Click Calculate to convert to a decimal. The first example has been entered for you. Click Reset and enter your own numbers.
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Try this matching exercise:

Quia - Java Games - Fraction Decimal Conversion

Fraction/Percent Conversion

Calculator Enter a fraction on the right hand side. Click Calculate to convert to percent. The first example has been entered for you. Click Reset and enter your own numbers.
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