{"id":35566,"date":"2025-06-24T12:24:54","date_gmt":"2025-06-24T12:24:54","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=35566"},"modified":"2025-06-24T12:24:55","modified_gmt":"2025-06-24T12:24:55","slug":"simplify-2-3-4-9-x-7-%c2%bd-9948-49-x-245","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/simplify-2-3-4-9-x-7-%c2%bd-9948-49-x-245\/","title":{"rendered":"Simplify: 2\/3 + 4\/9 x 7 \u00bd + 9948\/49 x 245."},"content":{"rendered":"\n

Simplify: 2\/3 + 4\/9 x 7 \u00bd + 9948\/49 x 245.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To simplify the expression:23+49\u00d7712+994849\u00d7245\\frac{2}{3} + \\frac{4}{9} \\times 7\\frac{1}{2} + \\frac{9948}{49} \\times 24532\u200b+94\u200b\u00d7721\u200b+499948\u200b\u00d7245<\/p>\n\n\n\n

Step-by-step Simplification<\/h3>\n\n\n\n

1. Convert all mixed numbers and perform multiplications first.<\/strong><\/p>\n\n\n\n

Convert<\/strong> 7127\\frac{1}{2}721\u200b to an improper fraction:712=1527\\frac{1}{2} = \\frac{15}{2}721\u200b=215\u200b<\/p>\n\n\n\n

Multiply<\/strong> 49\u00d7152\\frac{4}{9} \\times \\frac{15}{2}94\u200b\u00d7215\u200b:4\u00d7159\u00d72=6018=103\\frac{4 \\times 15}{9 \\times 2} = \\frac{60}{18} = \\frac{10}{3}9\u00d724\u00d715\u200b=1860\u200b=310\u200b<\/p>\n\n\n\n

Multiply<\/strong> 994849\u00d7245\\frac{9948}{49} \\times 245499948\u200b\u00d7245:<\/p>\n\n\n\n

Note that 245=5\u00d749245 = 5 \\times 49245=5\u00d749. So:994849\u00d7245=994849\u00d75\u00d749=9948\u00d75=49740\\frac{9948}{49} \\times 245 = \\frac{9948}{49} \\times 5 \\times 49 = 9948 \\times 5 = 49740499948\u200b\u00d7245=499948\u200b\u00d75\u00d749=9948\u00d75=49740<\/p>\n\n\n\n

Now add everything<\/strong>:23+103+49740=123+49740=4+49740=49744\\frac{2}{3} + \\frac{10}{3} + 49740 = \\frac{12}{3} + 49740 = 4 + 49740 = \\boxed{49744}32\u200b+310\u200b+49740=312\u200b+49740=4+49740=49744\u200b<\/p>\n\n\n\n

\n\n\n\n

Explanation <\/h3>\n\n\n\n

The original expression involves both fractions and whole numbers. To simplify accurately, it is essential to follow the order of operations, often remembered as PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).<\/p>\n\n\n\n

We begin by identifying all operations involved. The expression includes multiplication and addition. According to the rules of arithmetic, multiplication takes precedence over addition, so we perform those calculations first.<\/p>\n\n\n\n

First, convert the mixed number 7127\\frac{1}{2}721\u200b into an improper fraction. This is done by multiplying the whole number by the denominator and then adding the numerator. 7\u00d72+1=157 \\times 2 + 1 = 157\u00d72+1=15, so 712=1527\\frac{1}{2} = \\frac{15}{2}721\u200b=215\u200b. Now we multiply 49\\frac{4}{9}94\u200b by 152\\frac{15}{2}215\u200b. Multiplying the numerators and denominators gives us 6018\\frac{60}{18}1860\u200b, which simplifies to 103\\frac{10}{3}310\u200b.<\/p>\n\n\n\n

Next, we handle 994849\u00d7245\\frac{9948}{49} \\times 245499948\u200b\u00d7245. Here, recognizing that 245 is divisible by 49 makes the calculation simpler. Since 245=5\u00d749245 = 5 \\times 49245=5\u00d749, the multiplication simplifies: 994849\u00d75\u00d749\\frac{9948}{49} \\times 5 \\times 49499948\u200b\u00d75\u00d749. The 49s cancel out, leaving 9948\u00d75=497409948 \\times 5 = 497409948\u00d75=49740.<\/p>\n\n\n\n

Now add all the parts: 23+103=123=4\\frac{2}{3} + \\frac{10}{3} = \\frac{12}{3} = 432\u200b+310\u200b=312\u200b=4. Adding this to 49740 gives the final result:4+49740=497444 + 49740 = \\boxed{49744}4+49740=49744\u200b<\/p>\n\n\n\n

This process emphasizes the importance of simplifying step by step, recognizing number patterns, and respecting the proper order of operations.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Simplify: 2\/3 + 4\/9 x 7 \u00bd + 9948\/49 x 245. The Correct Answer and Explanation is: To simplify the expression:23+49\u00d7712+994849\u00d7245\\frac{2}{3} + \\frac{4}{9} \\times 7\\frac{1}{2} + \\frac{9948}{49} \\times 24532\u200b+94\u200b\u00d7721\u200b+499948\u200b\u00d7245 Step-by-step Simplification 1. Convert all mixed numbers and perform multiplications first. Convert 7127\\frac{1}{2}721\u200b to an improper fraction:712=1527\\frac{1}{2} = \\frac{15}{2}721\u200b=215\u200b Multiply 49\u00d7152\\frac{4}{9} \\times \\frac{15}{2}94\u200b\u00d7215\u200b:4\u00d7159\u00d72=6018=103\\frac{4 \\times 15}{9 \\times […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-35566","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35566","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=35566"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35566\/revisions"}],"predecessor-version":[{"id":35568,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35566\/revisions\/35568"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}