- \n
- A ratio<\/strong> compares two quantities using :`<\/strong>, to<\/strong>, or fraction<\/strong> form
\ud83d\udc49 Example: 2 : 3, 2 to 3, or 2\/3<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83e\udde0 Understanding Ratio Word Problems<\/h3>\n\n\n\n
Ratios can compare:<\/p>\n\n\n\n
- \n
- \ud83d\udc66\ud83d\udc67 People<\/strong> (boys : girls)<\/li>\n\n\n\n
- \ud83c\udf4e\ud83c\udf4c Objects<\/strong> (apples : bananas)<\/li>\n\n\n\n
- \u23f1\ufe0f Time, distance, money, or quantities<\/strong><\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83d\udd0d How to Compare Ratios (Step-by-Step)<\/h3>\n\n\n\n
- \n
- \ud83d\udcd6 Read carefully<\/strong> and identify the two ratios.<\/li>\n\n\n\n
- \ud83d\udd04 Write ratios in the same form<\/strong> (preferably fractions).<\/li>\n\n\n\n
- \u2696\ufe0f Make denominators the same<\/strong> (find equivalent ratios).<\/li>\n\n\n\n
- \u2797 Compare the numbers<\/strong> to decide which ratio is larger, smaller, or equal.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\n\u270f\ufe0f Example<\/h3>\n\n\n\n
- \n
- Ratio A: 3 boys : 5 girls \u2192 3\/5<\/strong><\/li>\n\n\n\n
- Ratio B: 4 boys : 6 girls \u2192 4\/6 = 2\/3<\/strong>
\ud83d\udc49 Compare 3\/5<\/strong> and 2\/3<\/strong>
\ud83d\udc49 2\/3 is greater<\/strong>, so Ratio B is larger \u2714\ufe0f<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83d\udd01 Using Equivalent Ratios<\/h3>\n\n\n\n
- \n
- Multiply or divide both terms by the same number<\/strong>
\ud83d\udc49 2 : 3 = 4 : 6 = 6 : 9<\/li>\n\n\n\n- Helps in easy comparison \ud83d\udc4d<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83d\udcc8 Cross-Multiplication Trick<\/h3>\n\n\n\n
For fractions a\/b<\/strong> and c\/d<\/strong>:<\/p>\n\n\n\n
- \n
- Multiply \ud83d\udc49 a \u00d7 d<\/strong> and b \u00d7 c<\/strong><\/li>\n\n\n\n
- Compare the results<\/li>\n<\/ul>\n\n\n\n
Bigger product = bigger ratio \u2b50<\/p>\n\n\n\n
\n\n\n\n\ud83e\udde9 Real-Life Applications<\/h3>\n\n\n\n
- \n
- \ud83c\udfeb Classroom strength (boys vs girls)<\/li>\n\n\n\n
- \ud83e\uddc3 Mixing juice (water : syrup)<\/li>\n\n\n\n
- \ud83d\udcb0 Comparing prices and discounts<\/li>\n\n\n\n
- \ud83d\ude97 Speed and distance problems<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\u26a0\ufe0f Common Mistakes to Avoid<\/h3>\n\n\n\n
- \n
- \u274c Comparing ratios with different units<\/strong><\/li>\n\n\n\n
- \u274c Not simplifying ratios<\/li>\n\n\n\n
- \u274c Ignoring the context of the problem<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n\ud83c\udf1f Quick Tip<\/h3>\n\n\n\n
\n
Always compare ratios in the same form and unit before deciding!<\/strong> \u2705<\/p>\n<\/blockquote>\n\n\n\n
Learn with an example<\/strong><\/p>\n\n\n\n
\n\n\n\u26ab A restaurant critic reviewed restaurants in Lowell and Morristown. In Lowell, the critic gave 18 positive reviews and 12 negative reviews. In Morristown, 19 of the reviews were positive and 13 were negative. In which city did the restaurant critic give a higher ratio of positive to negative reviews?<\/strong><\/p>\n\n\n\n
- \n
- Lowell<\/li>\n\n\n\n
- Morristown<\/li>\n\n\n\n
- neither; the ratios are equivalent<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n
The ratio of positive to negative reviews by the restaurant critic for Lowell was 18 to 12. The ratio for Morristown was 19 to 13.<\/p>\n\n\n\n
We want to figure out which ratio is higher: 18\/12 or 19\/13 .<\/p>\n\n\n\n
We can compare the ratios more easily if we express them as percentages.<\/p>\n\n\n\n
First write the ratio 18\/12 as a decimal. Then convert the decimal to a percentage.<\/p>\n\n\n\n
18\/12 = 1.5 = 150%<\/p>\n\n\n\n
Do the same thing for 19\/13 .<\/p>\n\n\n\n
19\/13 \u2248 1.46154 = 146.154%<\/p>\n\n\n\n
Now compare the percentages.<\/p>\n\n\n\n
150% ? 146.154%<\/p>\n\n\n\n
150% is larger than 146.154%.<\/p>\n\n\n\n
The restaurant critic gave a higher ratio of positive to negative reviews in Lowell.<\/p>\n<\/div><\/div>\n\n\n\n
\n\n\u26ab Last season, Emily’s soccer team won 6 games and lost 8 games. His cousin Amy’s team won 11 games and lost 20 games. Which team had a higher ratio of wins to losses?<\/strong><\/p>\n\n\n\n
- \n
- Emily’s team<\/li>\n\n\n\n
- Amy’s team<\/li>\n\n\n\n
- neither; the ratios are equivalent<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n
Last season, the ratio of wins to losses for Emily’s team was 6 to 8. The ratio for Amy’s team was 11 to 20.<\/p>\n\n\n\n
We want to figure out which ratio is higher: 6\/8 or 11\/20 .<\/p>\n\n\n\n
We can compare the ratios more easily if we express them as percentages.<\/p>\n\n\n\n
First write the ratio 6\/8 as a decimal. Then convert the decimal to a percentage.<\/p>\n\n\n\n
6\/8 = 0.75 = 75%<\/p>\n\n\n\n
Do the same thing for 11\/20<\/p>\n\n\n\n
11\/20 = 0.55 = 55%<\/p>\n\n\n\n
Now compare the percentages.<\/p>\n\n\n\n
75% ? 55%<\/p>\n\n\n\n
75% is larger than 55%.<\/p>\n\n\n\n
Emily’s team had a higher ratio of wins to losses.<\/p>\n<\/div><\/div>\n\n\n\n
\n\n\u26ab Tiana and Aaron are solicitors. Tiana averages 12 civil cases and 10 criminal cases annually. Meanwhile, Aaron averages 17 civil cases and 13 criminal ones. Which solicitor has a higher ratio of civil to criminal cases?<\/strong><\/p>\n\n\n\n
- \n
- Tiana<\/li>\n\n\n\n
- Aaron<\/li>\n\n\n\n
- neither; the ratios are equivalent<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n
For Tiana, the ratio of civil to criminal cases is 12 to 10. For Aaron, the ratio is 17 to 13.<\/p>\n\n\n\n
We want to figure out which ratio is higher: 12\/10 or 17\/13 .<\/p>\n\n\n\n
We can compare the ratios more easily if we express them as percentages.<\/p>\n\n\n\n
First write the ratio 12\/10 as a decimal. Then convert the decimal to a percentage.<\/p>\n\n\n\n
12\/10 = 1.2 = 120%<\/p>\n\n\n\n
Do the same thing for 17\/13 .<\/p>\n\n\n\n
17 \/13 \u2248 1.30769 = 130.769%<\/p>\n\n\n\n
Now compare the percentages.<\/p>\n\n\n\n
120% ? 130.769%<\/p>\n\n\n\n
130.769% is larger than 120%.<\/p>\n\n\n\n
Aaron has a higher ratio of civil to criminal cases.<\/p>\n<\/div><\/div>\n\n\n\n
let’s practice! \ud83d\udd8a\ufe0f<\/p>\n<\/div><\/div>\n\n\n\n
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<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"Compare ratios: word problems key notes : \ud83d\udd22 What is a Ratio? \ud83e\udde0 Understanding Ratio Word Problems Ratios can compare: \ud83d\udd0d How to Compare Ratios (Step-by-Step) \u270f\ufe0f Example \ud83d\udd01 Using Equivalent Ratios \ud83d\udcc8 Cross-Multiplication Trick For fractions a\/b and c\/d: Bigger product = bigger ratio \u2b50 \ud83e\udde9 Real-Life Applications \u26a0\ufe0f Common Mistakes to Avoid \ud83c\udf1fContinue reading “J.6 Compare ratios: word problems”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-202","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=202"}],"version-history":[{"count":10,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202\/revisions"}],"predecessor-version":[{"id":17653,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/202\/revisions\/17653"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- \u274c Comparing ratios with different units<\/strong><\/li>\n\n\n\n
- Compare the results<\/li>\n<\/ul>\n\n\n\n
- Helps in easy comparison \ud83d\udc4d<\/li>\n<\/ul>\n\n\n\n
- Ratio B: 4 boys : 6 girls \u2192 4\/6 = 2\/3<\/strong>
- \ud83d\udd04 Write ratios in the same form<\/strong> (preferably fractions).<\/li>\n\n\n\n
- \ud83c\udf4e\ud83c\udf4c Objects<\/strong> (apples : bananas)<\/li>\n\n\n\n
- \ud83d\udc66\ud83d\udc67 People<\/strong> (boys : girls)<\/li>\n\n\n\n