Study Guide For Unit 6 Test Fractions And Decimals

Study Guide for Unit 6 TestFractions and DecimalsFractions:Equivalent Fraction – Equivalent fractions are different fractions thatname the same number.Drawings can be used to find an equivalent fraction:To find an equivalent fraction with an algorithm multiply both the numerator anddenominator by the same number:Converting Improper fractions into mixed numbersHelpPractice 1In order to change from an improper fraction to a mixed number a drawing canhelp you see how many whole(s) and how much of a whole is left. This remainingamount will be then written as a fraction.Solution with Algorithm - Divide the denominator into the numerator. Thatnumber becomes the whole number found in the mixed number. The remainder

is made into a fraction (with denominator being the same as found in theimproper fraction). This is now a mixed number.Converting Mixed numbers into improper fractions Help 2Practice 1In order to change from a mixed number to an improper fraction a drawing canhelp you see how many fractional sections are in each whole and in theremainder. This then creates an improper fraction.Solution with Algorithm - Multiply the denominator by the whole number. Add inthe numerator to this total. This number is made into an improper fraction bykeeping the denominator the same as the original problem.Fractional Part of a Whole -Students will take a smaller part of a wholenumber. First, that whole needs to be divided into a certain number of groups(that number is shown in the denominator). The numerator shows how many ofthese groups are needed to solve this equation.Example: 2 of 243First, 24 needs to be divided into 3 groups(the denominator of 3 shows how many groups tomake). When 3 groups are created there are 8 ineach group(24 3 8). So, 1 of 24 8 .3Look at the equation’s numerator to find outhow many groups are needed. The numerator is2 so two groups are needed. That can be shownas 8 x 2 16 or 8 8 16. The answer to thisequation is 16.

Sorting Fractions – Two major landmarks (friendly numbers) are used insorting fractions: Fractions that are half or whole.When the denominator divided bythe numerator equals 2that fraction is half.When the numerator anddenominator are the same numberthat fraction is a whole.Examples: 4 , 6 , 108 12 20Examples: 7 , 12 , 25712 25Once these landmarks are found fractions can be sorted into several categories:less than one half (the numerator would be less than half of the denominator),half, more than half but less than whole (the numerator would be more than halfof the denominator but not equal), whole, and more than whole (the numeratorwould be larger than the denominator).Comparing Fractions – Students will compare two different fractions and placea , , or sign between them. For more help use the links below.Help with comparing fractions: Like denominators , like numerators, and unlike fractionsComparing fractions.with like denominators - When the denominatorsare the same you only have to compare the numerators. The larger numeratortells you that that is the larger fraction.with unlike denominators - When the denominators arenot the same follow these steps. Take the first fraction's numerator and multiplyit by the second fraction's denominator. Write that product on the left handside. Take the first fraction's denominator and multiply it by the second fraction'snumerator. Write that product on the right hand side. Now compare these twoproducts. If the product on the left is larger than the fraction on the left is thelarger one. If the product on the right is larger than that fraction is the largerone. If the products are equal then the fractions are equal.

4261248476 412 7Whole Number x Fraction - To solve this equation two strategies can beused: Add the fractions1 1 1 1 1 53 3 3 3 3 3this can be converted toAlgorithm Solution – Convert the whole number into an improperfraction. The fractions are then multiplied across.That answer can changed into a whole number to mixednumber.Decimals:Decimal Place Value - tens ones . tenths hundredthsStudents will be able to write the number for each place value given.Example: 54.69tenths – 6ones – 4hundredths- 9tens - 5Relating decimals to fractions – Students write each decimal as a fraction0.7 is the same as 7100.04 is the same as 41000.24 is the same as 24100

Drawing decimals using a 10 x 10 grid : Students will label grids, already filled in,with the decimal and fraction for that area filled in. Students will also be given ablank grid with a decimal number. They will then shade in that amount on thegrid, as well as write that decimal as a fraction.0.20.58Adding and subtracting decimals: At this point in the year students can usealgorithms to solve these equations. Other strategies can also be used to find theanswers. Equations can also be rewritten vertically to solve more easily.0.6 0.23 This could be written as 0.6 decimals should 0.23 line up before adding0.83Another strategy (using landmark #s) 0.23 0.2 0.030.6 0.2 0.80.8 0.03 0.31.34 0.7811This could be written as1.34 0.782.12Another strategy (using landmark #s)1.34 1.00 0.3 0.040.78 0.7 0.080.3 0.7 1.00.04 0.08 0.121.00 1.00 2.00 0.12 2.12

0.9 0.241This could be written as 0.9 0.241.14Another strategy (using landmark #s)0.24 0.2 0.040.9 0.2 1.1 0.04 1.14Runner’s Log – Students are given a target number (that includes a decimal),along with several numbers that they need to use. Using this information,students are to find out what decimals would best complete any blank entries.Example – The runner has logged in a total of 10.75 miles for the week. The logshows the following amounts: 2.3 0.75 1.08 1.86. There are also three blanksto add more mile amounts. One of the entries has the note- Raining hard whilerunning. Did not get to run for long.First, the number of miles already logged needs to be solved. Adding these 4amounts would 5.99. Students can either add up from that amount to reach10.75 or subtract 10.75 – 5.99 to find out how many miles still need to be loggedin. Students then need to create three more numbers to put on the blank entries.These can vary but the one that has the note about the rain would need to besmaller than the rest. All work is shown in this equation.

Comparing Fractions – Students will compare two different fractions and place a , , or sign between them. For more help use the links below. Help with comparing fractions: Like denominators , like numerators, and unlike fractions Comparing fractions.with like denom