Functional Skills Mathematics

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1 Functional Skills Mathematics Level Learning Resource Fractions N/L. N/L.

2 LEVEL Contents Numerator and Denominator N/L. Page Equivalent Fractions N/L. Pages - Comparing Fractions N/L. Pages - Improper Fractions and Mixed Numbers N/L. Pages - 0 Fractional Parts N/L. Pages - West Nottinghamshire College

3 LEVEL N/L. Information Numerator and Denominator Fractions are parts of something. The numerator is the top number in a fraction. This number tells us how many equal parts of the whole we have. The denominator is the bottom number in a fraction. This number tells us how many equal parts the whole has been divided into. numerator denominator The larger the denominator, the smaller each individual part. Examples is smaller than Exercise ) Arrange in order of size, starting with the smallest fractional part. ) Decide whether each of the following is true or false. is smaller than is smaller than ) Your friend has just had a small win on the lottery and has promised you a share. Would you rather have: c) West Nottinghamshire College

4 LEVEL N/L. Information Equivalent Fractions Fractions that have the same value or represent the same part of an object are equivalent fractions. They are worth the same. You can make equivalent fractions by multiplying or dividing the numerator and the denominator by the same number. Examples of the bar of chocolate is shaded. In these fractions, the numbers are different, yet the same portion has been shaded. Therefore is the same as. They are equivalent fractions. of the bar of chocolate is shaded. You can produce equivalent fractions by multiplying both the top and the bottom of the fraction by the same number. x x x x x x 0 x x West Nottinghamshire College

5 LEVEL N/L. Exercise Equivalent Fractions ) Draw arrows between equivalent fractions ) 0 0 In the fractions given, underline the fractions that are equivalent to. In the fractions given, circle the fractions that are equivalent to. ) Find the missing numbers. c) d) e) 0 f) West Nottinghamshire College

6 LEVEL N/L. Information Comparing Fractions If the denominators are all the same, then compare the numerators. When the numerator is bigger, the fraction is bigger. If the bottom numbers are not the same, then you need to change them to the same number before you can compare. You have to find a denominatoror which will fit them both. This number is called a common denominator. Examples Example - Which is the smallest? When all the numerators are the same, it is easy to see which is the smallest fraction. Example - Using a fraction wall to compare fractions. When you use a fraction wall, you can see straight away which is the smallest fraction. Example - Using the lowest common denominator to compare fractions. Find a number that, and (the denominators) all divide into. The number 0 is the common denominator for these fractions. Convert all the fractions to 0 as the common denominator and compare the numerators. x 0 x x x 0 x x West Nottinghamshire College

7 LEVEL N/L. Exercise Comparing Fractions Compare these fractions by using a method you are familiar with. ) Which is smaller? or or 0 c) or d) or ) Which is the largest? c) ) Put the following fractions in order, beginning with the smallest. c) 0 ) City Bank will lend you of your annual income, Urban Bank will allow you to borrow and Chapel Bank will lend you. Which bank will give you the biggest loan? ) Your brother has just won some money on a scratch card and has agreed to give you a share. Would you rather have or? West Nottinghamshire College

8 LEVEL N/L. Information Improper Fractions and Mixed Numbers An improper fraction is sometimes called a top heavy fraction because the top number of the fraction is greater than the bottom number. An improper fraction is worth more than a whole number. A mixed number is a whole number with a fraction. Examples Improper fractions e.g. 0 These fractions are all worth more than a whole. Therefore, the top number is bigger than the bottom number. Mixed number fractions e.g. These fractions are whole numbers and fractions. is the same as is the same as + + To convert to a mixed number, divide the bottom number into the top number. will be whole numbers and three parts left over i.e. whole To convert to an improper fraction, multiply the whole number by the bottom number of the fraction and add the fractional part. whole now add the other West Nottinghamshire College

9 LEVEL N/L. Exercise Improper Fractions and Mixed Numbers ) Convert these mixed numbers into improper fractions: c) d) e) f) g) h) 0 ) Convert these improper fractions to mixed numbers: c) d) e) f) g) 0 h) 0 ) Complete this table by converting from improper fractions to mixed numbers, or mixed numbers to improper fractions, where necessary. Improper fraction e.g. Mixed number e.g. West Nottinghamshire College

10 LEVEL N/L. Information Comparing Improper Fractions and Mixed Numbers When you are comparing improper fractions and mixed numbers, you must convert them to the same type of fraction. Examples Example To compare Make them all improper fractions then compare the numerators. Example To compare Make them all improper fractions If the denominators are different, convert to the same denominator. The lowest common denominator for these fractions is. Now compare the numerators. Exercise ) Put the following in order, beginning with the largest. c) d) e) West Nottinghamshire College 0

11 LEVEL N/L. Information Fractional Parts To find a fraction of a quantity: when the numerator is, divide by the denominator; when the numerator is not, divide by the denominator then multiply by the numerator. Example To find of something, divide by. of cm cm To find of something, divide by. of To find of something, divide by. of kg kg The bottom number tells you what to divide by. To find of something, divide by then multiply by. of To find of something, divide by then multiply by. of litres 0 litres Exercise ) Find of: c) d) e) ) Find of: c) d) e) ) Find of: c) d) 0 e) West Nottinghamshire College

LEVEL N/L. Exercise Fractional Parts ) What is of kg? ) What is 0 of 00 grams? ) What is of? ) What is of miles? ) What is of 0 litres? ) What is of kg? ) What is 0 of 00? ) What is of? ) What is of 0? 0) What is 0 of.

12 LEVEL N/L. Exercise Fractional Parts ) What is of kg? ) What is 0 of 00 grams? ) What is of? ) What is of miles? ) What is of 0 litres? ) What is of kg? ) What is 0 of 00? ) What is of? ) What is of 0? 0) What is 0 of.0? ) What is of 0 grams? ) What is of 0 litres? ) The soap factory has 0 employees. Two-thirds are men. How many are men? ) A caravan costs 00. A buyer has a loan for of the price. How much is the loan? ) Jenny is making 0 sandwiches for the party. are cheese. How many sandwiches are cheese? are tuna. How many sandwiches are tuna? c) The remainder are ham. How many are ham? West Nottinghamshire College

Accuplacer Arithmetic Review

Accuplacer Arithmetic Review Hennepin Technical College Placement Testing for Success Page Overview The Arithmetic section of ACCUPLACER contains 7 multiple choice questions that measure your ability to