{"id":39,"date":"2014-10-20T22:58:29","date_gmt":"2014-10-20T22:58:29","guid":{"rendered":"https:\/\/yellow-mathbelt.marjoriesayer.com\/?page_id=39"},"modified":"2014-10-24T16:59:46","modified_gmt":"2014-10-24T16:59:46","slug":"week-2-answers","status":"publish","type":"page","link":"https:\/\/yellow-mathbelt.marjoriesayer.com\/?page_id=39","title":{"rendered":"Week 2 – Answers"},"content":{"rendered":"

Week 2: Multiplication – Day 5<\/strong><\/p>\n

What is the missing number?<\/p>\n

1. 42 = 6 x 7 = ? x 14<\/p>\n

6 x 7 = 3 x 2 x 7 = 3 x 14<\/p>\n

So the missing number is 3.<\/p>\n

2. 52 = 2 x 26 = 4 x ?<\/p>\n

2 x 26 = 2 x 2 x 13 = 4 x 13<\/p>\n

So the missing number is 13.<\/p>\n

3. 84 = 7 x 12 = 21 x ?<\/p>\n

7 x 12 = 7 x 3 x 4 = 21 x 4<\/p>\n

So the missing number is 4.<\/p>\n

4. 48 = 8 x 6 = 16 x ?<\/p>\n

8 x 6 = 8 x 2 x 3 = 16 x 3<\/p>\n

So the missing number is 3.<\/p>\n

5. 72\u00a0= 8 x 9 = ? x 18<\/p>\n

8 x 9 = 4 x 2 x 9 = 4 x 18<\/p>\n

So the missing number is 4.<\/p>\n

\n

 <\/p>\n

Week 2: Multiplication – Day 4<\/strong><\/p>\n

Multiplication Patterns<\/p>\n

1. How can you tell if a number is a multiple of ten?<\/p>\n

Its ones digit is zero. Examples of multiples of ten: 10, 100, 3240, 9600<\/p>\n

2. How can you tell if a number is a multiple of five?<\/p>\n

Its ones digit is either zero or five. Examples of multiples of five: 5, 15, 105, 7050<\/p>\n

3. Write down the multiples of 11 from 1 x 11 to 9 x 11.<\/p>\n

11, 22, 33, 44, 55, 66, 77, 88, 99<\/p>\n

4. The ones-digits for multiples of nine follow a pattern. What is the pattern?<\/p>\n

The first ten multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.<\/p>\n

The pattern of the ones-digits is 9, 8, 7, 6, 5, 4, 3, 2, 1, 0. This pattern is repeated for the next ten multiples, over and over.<\/p>\n

5. A power of nine is a multiple of nine by itself. The first power of nine is 9. The second power of 9 is 9×9. The third power of nine is 9x9x9. The ones-digits of powers of nine form a pattern. What is the pattern?<\/p>\n

The first power of 9 is 9. The second power is 81. The third power is 729. Multiplying 729 by 9 would have a ones-digit of 1. The next power of 9 would then have a ones-digit of 9.<\/p>\n

The pattern is 9, 1, 9, 1, 9, 1 and so on. Alternating 9s and 1s.<\/p>\n

Bonus question: of the numbers from 1 through 8, what are the patterns of ones-digits of their powers?<\/p>\n

\n

 <\/p>\n

Week 2: Multiplication – Day 3<\/strong><\/p>\n

1.\u00a0What are the factors of 9?<\/p>\n

The factors of 9 are 1, 9, and 3.<\/p>\n

2. Is 3 a factor of 21?<\/p>\n

Yes, 3 is a factor of 21 because 3 x 7 = 21.<\/p>\n

3. Is 6 a factor of 33?<\/p>\n

No. 33 is in between two multiples of 6. 33 divided by 6 is 5 with remainder 3.\u00a06 x 5 = 30 and 6 x 6 = 36, and 33 is between.<\/p>\n

4. What are all of the factors of 42?<\/p>\n

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.<\/p>\n

In pairs: 1 and 42; 2 and 21; 3 and 14; 6 and 7.<\/p>\n

5.\u00a0Every counting number has\u00a0at least two factors<\/strong>. What are these two factors?<\/p>\n

(A counting number is a positive whole number, such as 1, 2, 3, 4, 5, 6, and so on.) For example, what are the two factors of 7?<\/p>\n

1 is a factor of every number. And every number is a factor of itself.<\/p>\n

The two factors of 7 are 1 and 7.<\/p>\n

\n

 <\/p>\n

Week 2: Multiplication – Day 2<\/strong><\/p>\n

\"multi-area-answers\"<\/a><\/p>\n

 <\/p>\n

Notice that adding and multiplying look quite different! Draw some more pictures of adding vs. multiplying.<\/p>\n

\n

 <\/p>\n

Week 2: Multiplication – Day 1<\/p>\n

1. \u00a0 \u00a022 x 10 = 220<\/p>\n

2. \u00a0 \u00a0 3 x 22 = \u00a066<\/p>\n

3. \u00a0 \u00a0 3 x 220 =\u00a0660<\/p>\n

4. \u00a0 \u00a010 x 14 =\u00a0140<\/p>\n

5. \u00a0 \u00a0 9 x 14 =\u00a0140 – 14 = 140 – 10 – 4 = 130 – 4 = 126<\/p>\n","protected":false},"excerpt":{"rendered":"

Week 2: Multiplication – Day 5 What is the missing number? 1. 42 = 6 x 7 = ? x 14 6 x 7 = 3 x 2 x 7 = 3 x 14 So the missing number is 3. 2. 52 = 2 x 26 = 4 x ? 2 x 26 = 2 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":12,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-39","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages\/39","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=39"}],"version-history":[{"count":7,"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages\/39\/revisions"}],"predecessor-version":[{"id":75,"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages\/39\/revisions\/75"}],"up":[{"embeddable":true,"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages\/12"}],"wp:attachment":[{"href":"https:\/\/yellow-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=39"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}