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MATHS FACTS YOU NEED TO KNOW It will really help you improve your Maths if you learn all these facts! Have a go and then try to test yourself!! Fractions, Decimals, Percentages FRACTION DECIMAL PERCENTAGE 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 10/10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Fractions, Decimals and Percentages FRACTION 1/4 1/2 3/4 1/5 2/5 3/5 4/5 DECIMAL 0.25 0.5 0.75 0.2 0.4 0.6 0.8 PERCENTAGE 25% 50% 75% 20% 40% 60% 80% Test Yourself • Write 4/10 as a decimal. • What is 3/5 as a decimal? • Write 0.53 as a percentage. • What is 75% as a fraction? • Write ¼ as a percentage. • What is ½ as a decimal? • What is ½ as a percentage? • Write ¾ as a decimal. Answers •Write 4/10 as a decimal. 0.4 • What is 3/5 as a decimal? 0.6 • Write 0.53 as a percentage. 53% • What is 75% as a fraction? 3/4 • Write ¼ as a percentage. 25% • What is ½ as a decimal? 0.5 • What is ½ as a percentage? 50% • Write ¾ as a decimal. 0.75 Ordering Decimals • To order a set of decimals, write them out directly underneath each other. • Add place holders so each number has the same amount of digits • Starting with the biggest number, look at each column in turn to work out the order Test yourself! Order these sets of numbers, smallest first: • 2.75, 27.5, 2.72. 2.277, 22.727 • 11.1, 11.11, 11.011, 11.101, 11.01 • 217.71, 217.17, 271.071, 271.017, 271 • 0.28, 0.288, 0.208, 2.8, 2.801 Answers Order these sets of numbers, smallest first: • 2.75, 27.5, 2.72. 2.277, 22.727 2.277, 2.72, 2.75, 22.727, 27.5 • 11.1, 11.11, 11.011, 11.101, 11.01 11.01, 11.011, 11.1, 11.101, 11.11 • 217.71, 217.17, 271.071, 271.017, 271 217.17, 217.71, 271, 271.017, 271.071 • 0.28, 0.288, 0.208, 2.8, 2.801 0.208, 0.28, 0.288, 2.8, 2.801 Ordering mixed fractions, decimals and percentages • Always convert everything to either all fractions, all decimals or all percentages. • 5/10, 48%, 0.45, 3/5, 35% Convert them all to a percentage 50%, 48%, 45%, 60%, 35% Then it is easy to order them! Test yourself! Put these in order, starting with the smallest: • 2/5, 43%, 0.25, 2/10, 20% • ¼, 3/10, 2/5, 50%, 0.3 • 33%, 8/10, 2/5, ¾, 0.85 Test yourself! Put these in order, starting with the smallest: • 2/5, 43%, 0.25, 2/10, 20% • ¼, 3/10, 2/5, 50%, 0.3 • 33%, 8/10, 2/5, ¾, 0.85 Answers Put these in order, starting with the smallest: • 2/5, 43%, 0.25, 2/10, 26% 2/10, 0.25, 26%, 2/5, 43% • ¼, 3/10, 2/5, 50%, 0.32 ¼, 3/10, 0.32, 2/5, 50% • 33%, 8/10, 2/5, ¾, 0.85 33%, 2/5, ¾, 8/10, 0.85 Equivalent fractions • If a fraction is equivalent to ½, the top number will always be half the bottom number. • 3/6, 7/14, 10/20, 40/80, 5/10 all all equivalent fractions Equivalent fractions • To find an equivalent fraction you need to multiply or divide the top and bottom by the same number. • E.g. To find equivalent fractions for 4/6: multiply the top and bottom by 5 = 20/30, multiply the top and bottom by 3 = 12/18 Simplifying fractions • To simplify a fraction you need to find the biggest number you can equally divide the top and bottom by. • E.g. To simplify 5/15, divide the top and bottom by 5 = 1/3 • To simplify 40/90, divide the top and bottom by 10 = 4/9 Test yourself! • Simplify these fractions: - 4/6 - 20/50 - 18/27 • True or false? 15/40 is equivalent to ½. Explain your answer. • True or false? 30/90 is equivalent to 1/3. Explain your answer. Answers • Simplify these fractions: - 4/6 2/3 (divide top and bottom by 2) - 20/50 2/5 (divide top and bottom by 10) - 18/27 2/3 (divide top and bottom by 9) • True or false? 15/40 is equivalent to ½. Explain your answer. False, 15 is not half of 40 and if you simplify 15/40, it is 3/8. • True or false? 30/90 is equivalent to 1/3. Explain your answer. True, if you divide 30 and 90 by 30 it is 1/3 Negative Numbers • Always think of negative numbers as temperature to help you • The bigger the negative number, the colder it is • The smaller the negative number, the warmer it is Negative Numbers •Always, always use a number line to add or subtract negative numbers -3 + 6 = 3 0 – 2 = -2 -2 + 9 = 7 7 – 10 = -3 Test yourself! • What is 7 less than 3? • What is -5 + 10? • The temperature on Monday was -2. On Tuesday the temperature rose by 8 degrees. What was the temperature on Tuesday? • The temperature on Monday was 1 degree. It fell by 2 degrees each day. What was the temperature on Friday? Answers • What is 7 less than 3? -4 • What is -5 + 10? 5 • The temperature on Monday was -2. On Tuesday the temperature rose by 8 degrees. What was the temperature on Tuesday? 6 degrees • The temperature on Monday was 1 degree. It fell by 2 degrees each day. What was the temperature on Friday? -7 degrees