Revision on fractions and decimals

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Julius Parks
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1 Revision on fractions and decimals Fractions 1. Addition and subtraction of fractions (i) For same denominator, only need to add the numerators, then simplify the fraction Example 1: " + $ " = &$ " (they have the same denominator) = ' " = ( (ii) For different denominators, find the LCM of the denominators, then change the fraction by multiply the same factor to the numerator and the denominator, then do the same as for same denominator. Example 2: + $ ( " = $ ( $ + $ ( " ( = $ $, +, $, = - $, (they do not have the same denominator) (Find the LCM of 12 and 18 first, which is 36 and expand both fractions so that they have same demonstrator) = ' For fractions with mixed numbers, we do the whole number part and the fractions part separately. Example 3: (there are mixed numbers) ( 0 = (2 + 1)( + ) ) (do the whole number part and fraction part separately) ( 0 = = (,M,M = 3 N,M (Find the LCM of 12 and 5 first, which is 60 and expand both fractions so they have the same denominator)

2 2. Multiplication of fractions For proper fractions, we just need to multiply the numerators and the denominators. Example 4: " $ " = $ " " = $,' (they don t have common factors) If there are common factors from the numerators and denominators, simplify them before multiply. Example 5: $ ( ' = $ $ ( $ ' = ' ' = 0, (they have common factors) (simplify the numbers with common factor first) (Final answer) For fractions with mixed numbers, we need to change the mixed number into improper fractions first. Example 6: 2 1 (there are mixed numbers) ( 0 = ( (& 0& ( 0 (, 0 0,, (, 0 0 (convert the mixed number into improper fractions first) (they have common factors from numerators and denominators) (simplify with the common factors first) = 0 ( = 0 ( = 2 ( (change the number back to mixed number and its most simplify form) 3. Division of fractions Remember the song Keep Change flip Keep the first fraction, change the division ( ) sign to multiplication ( ) sign, then flip the second fractions Example 7: (for proper fractions) " $ " = " " $ = " (' = $ (keep, change, flip)

3 Example 8: (for fractions with mixed numbers) 2 1 (there are mixed numbers) (, = ( (&,& (, ( N, (, N,, (, N ( N ' = 1 ' (convert the mixed number into improper fractions first) (keep change flip) (simplify with the common factors first) (change the number back to mixed number and its most simplify form) 4. Mixed operations and word problems Mixed operations: follow the BIDMAS, then all the above rules Word problems: form an expression (in horizontal form first, then work out the answer and write a sentence as a final answer. 5. How can you find required amount from existing recipe? For example: (i) if the recipe says that the ingredients can serve 5 people, but you need to serve 20 people, then you need to multiply all ingredients by 4 to create your own recipe with correct ingredients. (ii) if the recipe says that the ingredients can serve 50 people, but you need to serve 20 people, then you need to divide the ingredients by 50 then times 20, or just simply times a fraction ( 0.

4 Decimals 1. Addition and subtraction of decimals Line up the decimals points then do as normal addition and subtraction Example 1: = Example 2: = Multiplication of decimals You don't need to line up the decimals points or add zero. You just need to multiple the numbers as usual. Then estimate or count the decimals points of the numbers to decide where should you put the decimal point in your final answer. Example 3: = *Where should I put the decimals point 1. since 12 7 =84, therefore I put the decimal point after since both of the number have 1 decimal place, that is a total of 2 decimals place for the final answer (start counting from the last digit of your answer. 3. Division of decimals If the divisor (or denominator) is a whole number, follow the decimal point of that number, then do as normal division. Example 4: = ) If the divisor is not a whole number, times both the dividend and the divisor to a power of 10 to make it into a whole number, then do as normal division. Example 5: = ) = =

5 4. Mixed operations and word problems Mixed operations: follow the BIDMAS, then all the above rules Word problems: form an expression (in horizontal form first, then work out the answer and write a sentence as a final answer. 5. Rounding of decimals You might round to a specific decimal place (3 d.p.) or to a special place value (nearest tenths) 6. How and when to decide the rounding of decimal place? Think about the followings: Why do you need to round the decimals? a. Is it too many decimals points? b. Is that no need or meaningless to include so many decimals points? c. Is there really that currency in the real life for the decimals money we have calculated? When do you need to round the decimals? a. Do I round the original prize before multiply the amount of ingredient? Why? b. Do I round the final answer only? Why? Using a calculator You are encouraged to bring in your own calculation. Scientific calculation is preferred but not a must for this assessment. You are not allowed to borrow / share calculators within the assessment time.

Student Success Center Arithmetic Study Guide for the ACCUPLACER (CPT)

Student Success Center Arithmetic Study Guide for the ACCUPLACER (CPT) Fractions Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) is parts have a dot out of Proper fraction: