Ratio and Proportion Notes PDF

**[RATIO]** -- **is defined as the comparison of two quantities of the same units.** **[UNIT RATIO]**-- - **a ratio with a denominator of 1.** **Ratio Formula** **We use the [ratio formula](https://www.cuemath.com/ratio-formula/) while comparing the relationship between two numbers or quantities....

**[RATIO]** -- **is defined as the comparison of two quantities of the same units.** **[UNIT RATIO]**-- - **a ratio with a denominator of 1.** **Ratio Formula** **We use the [ratio formula](https://www.cuemath.com/ratio-formula/) while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say \'a\' and \'b\' is a: b, which is read as \'a is to b\'.** **WAYS ON WRITING RATIO (note: Always remember that in writing ratio the first quantity must be written first followed by the second quantity).** **FRACTION COLUMN FORM WORD FORM** [\$\\frac{\\mathbf{1}}{\\mathbf{2}}\$]{.math.inline} **1:2 1 is to 2** **Ratios can be classified into two types** - **Part to Part Ratio** - denotes how two distinct entities or groups are related. FOR EXAMPLE: **Ratio** **green apples : red apples** **3 : 9 in simplest form 1:3** - **Part to Whole Ratio** - denotes the relationship between a specific group to a whole. Example: **What is the ratio of girls to the number of all the students?** EXAMPLE: There are 18 boys and 6 girls in a class a. What ratio is the number of boys to the number of girls? SOLUTION BOYS : GIRLS = 18:6 OR 3 boys in every 6 girls b. How many times as many boys as girls are there in the class? Solution: 3 x 6(girls) = 18 boys 3 times One molecule of glucose contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. What is the ratio of hydrogen atoms to the total number of atoms in the molecule? Solution: Hydrogen:total numbers of atoms 12:24 A bin at a hardware store contains 120 washers and 85 bolts. Write the ratio of washers to bolts in simplest form. solution : washers: bolt 120: 85 in simplest form 24:17 ( both number can be divided by 5) **[PERCENTAGE]** - comes from the Latin word centum means "parts per hundred". **[Converting Decimal to Percent]** - A value can be converted into a percentage value by [multiplying it with 100 and placing a percentage (%).] Multiplying a decimal by 100 **shifts the decimal point by two places towards the right.**  0.657 = 65.7% **[Converting Percent to Decimal]** - Percent to decimal conversion is done by removing the % symbol and dividing it with 100. Dividing 100 **shifts the decimal point two places towards the left.** 723.29% = 0.2329 **[Converting Fraction to Percent]** - Converting a fraction to percent is done by multiplying the given fraction by 100 and simplifying it further. **[Converting Percent to Fraction]** - The percent value has to be changed in a number in fractional form by removing the percent symbol and dividing it by 100.  **PROPORTION** PROPORTION - an equation in which **[two] [ratios are set equal to each other.]** **[PROPORTION]** **a:b = c:d** - **Where the outer terms a and d are the "extremes" and the middle terms b and c are the "means"** **TO DETERMINE IF THE GIVEN IS A PROPORTION WE JUST CROSS MULTIPLY THE GIVEN , IF THE ANSWERS ARE EQUAL THEN IT IS A PROPORTION.** **Steps in Solving Proportions (Solving for Unknowns)** 1.Calculate the cross products. 2\. Set the cross products equal to each other. 3\. Solve the equation. For examples: 1. **2 : x = 3 : 9** \ [\$\$\\frac{\\mathbf{9}}{\\mathbf{6}}\\mathbf{=}\\frac{\\mathbf{x}}{\\mathbf{10}}\\mathbf{\\ = 6x\\ = 90\\ =}\\frac{\\mathbf{6x}}{\\mathbf{6}}\\mathbf{=}\\frac{\\mathbf{90}}{\\mathbf{6}}\\mathbf{\\ x\\ = \\ 15}\$\$]{.math.display}\ **[Solving Percentage Problems]** - Another simple method commonly used to solve percent problems is using PROPORTION. **[FORMULA : ]** \ [\$\$\\frac{percent\\ (\\%)}{100}\\ = \\ \\frac{part\\ (\\ of\\ a\\ number)}{whole\\ /\\ total}\$\$]{.math.display}\ For examples: 1. What percent of 60 is 80? Given: 60 part 80 whole Being asked: percent ( let x ) \ [\$\$\\frac{x\\ \\ (\\%)}{100}\\ = \\ \\frac{60\\ \\ \\ (\\ of\\ a\\ number)}{80\\ \\ total}\$\$]{.math.display}\ \ [\$\$\\frac{30\\ (\\%)}{100}\\ = \\ \\frac{21\\ (\\ of\\ a\\ number)}{\\text{x\\ \\ total}}\$\$]{.math.display}\ **30x = 2100 =**[\$\\frac{\\mathbf{30x}}{\\mathbf{30}}\\mathbf{\\ =}\\frac{\\mathbf{\\ 2100}}{\\mathbf{30}}\\mathbf{= \\ x\\ =}\$]{.math.inline}**70**