MTE 280 Test 2

When we say a is divisible by b, if another number c cxb=aExample: 24 is divisible by 2 because there is another number that will be multiplied by 2 to get 24. 10 is divisible by 55 divides 105 is a divisor of 10 10 is a multiple of 5 5 and 2 are factors of 10 Ending of a number: by 2, 5, 10 Look at end of number if it is divisible Find sum of number: by 3, 6, 9 Add all the numbers example: 3+9+6=16 so find what’s divisible by 16 Last two digits: by 4 Use the last two numbers to see what’s divisible Last three digits: by 8 use the last 3 numbers to find what’s divisible Double the last number: by 7Multiply the last digit by 2 and then subtract Chop off: by 11chop off the last 2 numbers and then add it by the rest of the numbers

Prime factorization is used to find the LCM 24: 1,2,3,4,6,8,12,2424=2*2*2*324=2^3*3GCF36=2*2*3*3What is the GCF of 24 and 36? 24=2*2*2*336=2*2*3*3GCF=2*2*3=12List method of GCF 24: 1,2,3,4,6,8,12,2436: 1,2,3,4,6,9,12,18,36GCF=12 List Method of LCM 24: 24,48,7236: 36,72LCM=72

What is a fraction? A symbol of the relationship between a part of a whole Ratio example: boys:studentsEven if you do use the LCM to find a common denominator, it still won’t give you the simplest form for the answer. Dividing a fraction Leave it, change it, flip it.

Different denominatorsfind the least common multiple of 1/4+1/64,8,12,16,20,24,28,32,6,12,18,24,30,361/4*6 + 1/6*4 6/24+4/24 =10/24=5/12

Problem solving example: Marc opened a pizza box. Inside there was 3/4 of a pizza. Marc ate 1/2 of what was in the box. How much pizza did Marc eat? Answer: he ate 3/8Janice is preparing a recipe that calls for 3/4 of a cup of oil per serving. If Janice needs to prepare 2 and 2/3 servings, how many cups of oil will she need? 1 serving: 3/4 She will need 2 cups

A set of marbles can be divided in equal shares among 2, 3, 4, 5, or 6 children with no marbles left over, what is the least number of marbles this set could have? 2:2,4,6,8,10….. 603: 3,6,9,12,15,18…..604:4,8,12,16……605: 5,10,15,20,25…..606: 6,12,18,24,30….60 The least number of marbles this set could have is 60

1)There was 3/4 of a pie in the refrigerator. John ate 2/3 of the left over pie. How much pie did he eat? He ate 1/2 of the whole pie 2) Three-fourths of the class are girls. Two-thirds of the girls have black hair. What fraction of the class is female and dark haired? 1/4+1/4=2/4=1/21/2 of the class are girls and have black hair.